A recursive algorithm is adopted for the computation of dyadic Green＇s functions in three-dimensional stratified uniaxial anisotropic media with arbitrary number of layers. Three linear equation groups for computing ...A recursive algorithm is adopted for the computation of dyadic Green＇s functions in three-dimensional stratified uniaxial anisotropic media with arbitrary number of layers. Three linear equation groups for computing the coefficients of the Sommerfeld integrals are obtained according to the continuity condition of electric and magnetic fields across the interface between different layers, which are in correspondence with the TM wave produced by a vertical unit electric dipole and the TE or TM wave produced by a horizontal unit electric dipole, respectively. All the linear equation groups can be solved via the recursive algorithm. The dyadic Green＇s functions with source point and field point being in any layer can be conveniently obtained by merely changing the position of the elements within the source term of the linear equation groups. The problem of singularities occurring in the Sommerfeld integrals is efficiently solved by deforming the integration path in the complex plane. The expression of the dyadic Green＇s functions provided by this paper is terse in form and is easy to be programmed, and it does not overflow. Theoretical analysis and numerical examples show the accuracy and effectivity of the algorithm.展开更多
Since the Leibniz-Newton formula for derivatives cannot be used in local fields, it is important to investigate the new concept of derivatives in Walsh-analysis, or harmonic analysis on local fields. On the basis of i...Since the Leibniz-Newton formula for derivatives cannot be used in local fields, it is important to investigate the new concept of derivatives in Walsh-analysis, or harmonic analysis on local fields. On the basis of idea of derivatives introduced by Butzer, Schipp and Wade, Weisz has proved that the maximal operators of the one-dimensional dyadic derivative and integral are bounded from the dyadic Hardy space Hp,q to Lp,q, of weak type （L1,L1）, and the corresponding maximal operators of the two-dimensional case are of weak type （Hi, L1）. In this paper, we show that these maximal operators are bounded both on the dyadic Hardy spaces Hp and the hybrid Hardy spaces H^#p 0〈p≤1.展开更多
Dyadic coping plays an important role in older adults with mild cognitive impairment and their spouses. Significant correlations were found between dyadic coping and self-efficacy, anxiety and depression, marital qual...Dyadic coping plays an important role in older adults with mild cognitive impairment and their spouses. Significant correlations were found between dyadic coping and self-efficacy, anxiety and depression, marital quality, and quality of life in elderly patients with mild cognitive impairment and their spouses, and there were gender differences, with a 36.1% [P = 0.028, OR = 0.639, 95% CI (0.429, 0.952)] and 54% [P = 0.004, OR = 0.460, 95% CI (0.269, 0.785)] reduction in the risk of MCI and dementia for older men aged 65 - 69 years with a spouse and for those aged 80 years and older with a spouse, respectively. In contrast, there was no significant difference in the association between having or not having a spouse and developing MCI and dementia in older women (all P > 0.05). Psychosocial interventions, skills interventions, and exercise from the perspective of dyadic relationships were effective in improving the physical and mental health of older adults with mild cognitive impairment and their spouses. However, there is a lack of specific intervention programs for dyadic relationships in the local cultural context as an entry point. Therefore, it is necessary to draw on internal and external relevant literature to treat both partners as a whole for intervention, provide personalized social, cognitive and motor therapy for patients and promote the integration and participation of caregivers, help patients and spouses to improve the sense of well-being and intimacy, reduce the burden of caregivers, and build a dyadic coping intervention program suitable for elderly patients with mild cognitive impairment in China. The current article aims to provide a conceptual review focusing on dyadic coping care to inform the development of a dyadic intervention program suitable for older adults with mild cognitive impairment in China. This review outlines the theoretical concepts, assessment tools, current state of research, and intervention methods for mild cognitive impairment and dyadic coping.展开更多
Automatic feature extraction and classification algorithm of echo signal of ground penetrating radar is presented. Dyadic wavelet transform and the average energy of the wavelet coefficients are applied in this paper ...Automatic feature extraction and classification algorithm of echo signal of ground penetrating radar is presented. Dyadic wavelet transform and the average energy of the wavelet coefficients are applied in this paper to decompose and extract feature of the echo signal. Then, the extracted feature vector is fed up to a feed forward muhi layer perceptron classifier. Experimental results based on the measured GPR, echo signals obtained from the Mei shan railway are presented.展开更多
Micro triadic structure is an important motif and serves the building block of complex networks.In this paper,the authors define structure entropy for a social network and explain this concept by using the coded triad...Micro triadic structure is an important motif and serves the building block of complex networks.In this paper,the authors define structure entropy for a social network and explain this concept by using the coded triads proposed by Davis and Leinhardt in 1972.The proposed structure entropy serves as a new macro-evolution index to measure the network’s stability at a given timestamp.Empirical analysis of real-world network structure entropy discloses rich information on the mechanism that yields given triadic motifs frequency distribution.This paper illustrates the intrinsic link between the micro dyadic/triadic motifs and network structure entropy.Importantly,the authors find that the high proportion of reciprocity and transitivity results in the emergence of hierarchy,order,and cooperation of online social networks.展开更多
Homogeneous binary function products are frequently encountered in the sub-universes modeled by databases,spanning from genealogical trees and sports to education and healthcare,etc.Their properties must be discovered...Homogeneous binary function products are frequently encountered in the sub-universes modeled by databases,spanning from genealogical trees and sports to education and healthcare,etc.Their properties must be discovered and enforced by the software applications managing such data to guarantee plausibility.The(Elementary)Mathematical Data Model provides 17 types of dyadic-based homogeneous binary function product constraint categories.MatBase,an intelligent data and knowledge base management system prototype,allows database designers to simply declare them by only clicking corresponding checkboxes and automatically generates code for enforcing them.This paper describes the algorithms that MatBase uses for enforcing all 17 types of homogeneous binary function product constraint,which may also be employed by developers without access to MatBase.展开更多
Let n≥2 be an integer. We give necessary and sufficient conditions for an integral quadratic form over dyadic local fields to be n-universal by using invariants from Beli's theory of bases of norm generators.Also...Let n≥2 be an integer. We give necessary and sufficient conditions for an integral quadratic form over dyadic local fields to be n-universal by using invariants from Beli's theory of bases of norm generators.Also, we provide a minimal set for testing n-universal quadratic forms over dyadic local fields, as an analogue of Bhargava and Hanke's 290-theorem(or Conway and Schneeberger's 15-theorem) on universal quadratic forms with integer coefficients.展开更多
The single 2 dilation wavelet multipliers in one-dimensional case and single A-dilation （where A is any expansive matrix with integer entries and [detA[ = 2） wavelet multipliers in twodimen- sional case were complet...The single 2 dilation wavelet multipliers in one-dimensional case and single A-dilation （where A is any expansive matrix with integer entries and [detA[ = 2） wavelet multipliers in twodimen- sional case were completely characterized by Wutam Consortium （1998） and Li Z., et al. （2010）. But there exist no results on multivariate wavelet multipliers corresponding to integer expansive dilation matrix with the absolute value of determinant not 2 in L^2（R^2）. In this paper, we choose 2I2 = （02 20 ） as the dilation matrix and consider the 212-dilation multivariate wavelet ψ = {ψ1, ψ2, ψ3 } （which is called a dyadic bivariate wavelet） multipliers. Here we call a measurable function family f ={fl, f2, f3} a dyadic bivariate wavelet multiplier if ψ1 = （F^-1（f1ψ1）,F^-1（f2ψ2）, F-l（f3ψ3）} is a dyadic bivariate wavelet for any dyadic bivariate wavelet ψ = {ψ1, ψ2, ψ3}, where f and F^- 1 denote the Fourier transform and the inverse transform of function f respectively. We study dyadic bivariate wavelet multipliers, and give some conditions for dyadic bivariate wavelet multipliers. We also give concrete forms of linear phases of dyadic MRA bivariate wavelets.展开更多
In this paper, we present a new technique for mammogram enhancement using fast dyadic wavelet transform （FDyWT） based on lifted spline dyadic wavelets and normalized Tsallis entropy. First, a mammogram image is deco...In this paper, we present a new technique for mammogram enhancement using fast dyadic wavelet transform （FDyWT） based on lifted spline dyadic wavelets and normalized Tsallis entropy. First, a mammogram image is decom- posed into a multiscale hierarchy of low-subband and high-subband images using FDyWT. Then noise is suppressed using normalized Tsallis entropy of the local variance of the modulus of oriented high-subband images. After that, the wavelet coefficients of high-subbands are modified using a non-linear operator and finally the low-subband image at the first scale is modified with power law transformation to suppress background. Though FDyWT is shift-invariant and has better poten- tial for detecting singularities like edges, its performance depends on the choice of dyadic wavclcts. On the other hand, the nulnber of vanishing moments is an important characteristic of dyadic wavelets for singularity analysis because it provides an upper bound measurement for singularity characterization. Using lifting dyadic schemes, we construct lifted spline dyadic wavelets of different degrees with increased number of vanishing moments. We also examine the effect of these wavelets on mammogram enhancement. The method is tested on mammogram images, taken from MIAS （Mammographic Image Analysis Society） database, having various background tissue types and containing different abnormalities. The comparison with tile state-of-the-art contrast enhancement methods reveals that the proposed method performs better and the difference is statistically significant.展开更多
The principles of the new maximal operator H＊ we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz L^Xp.q[0,1） to the Lorentz L^Xp.q[0,1） for 1/2〈 p〈∞, 0〈~ q ≤ ∞, where X is any...The principles of the new maximal operator H＊ we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz L^Xp.q[0,1） to the Lorentz L^Xp.q[0,1） for 1/2〈 p〈∞, 0〈~ q ≤ ∞, where X is any Banach space. When the Banach space X has the RN property, the sequence dnHnf converges to f a.e. Meanwhile the convergence in L^Xp norm for 1≤p〈∞ is a consequence of that the family functions K （n∈N） is an approximate identity.展开更多
In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I＊ and Cesàro mean operator σ＊ are bounded from the B-valued martingale Hardy spaces pΣα, Dα,...In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I＊ and Cesàro mean operator σ＊ are bounded from the B-valued martingale Hardy spaces pΣα, Dα, pLα, p H#α, pKr to Lα （0 α ∞）, respectively. The facts show that it depends on the geometrical properties of the Banach space.展开更多
In this paper, we construct a class of nowhere differentiable continuous functions by means of the Cantor series expression of real numbers. The constructed functions include some known nondifferentiable functions, s... In this paper, we construct a class of nowhere differentiable continuous functions by means of the Cantor series expression of real numbers. The constructed functions include some known nondifferentiable functions, such as Bush type functions. These functions are fractal functions since their graphs are in general fractal sets. Under certain conditions, we investigate the fractal dimensions of the graphs of these functions, compute the precise values of Box and Packing dimensions, and evaluate the Hausdorff dimension. Meanwhile, the Holder continuity of such functions is also discussed.展开更多
The aim of this paper is to prove the following theorem concerning the term by term differentiation the-orem of Walsh-Kaczmarz series. Let (ck) be a decreasing real sequence withare integrable functions and f(x) is a....The aim of this paper is to prove the following theorem concerning the term by term differentiation the-orem of Walsh-Kaczmarz series. Let (ck) be a decreasing real sequence withare integrable functions and f(x) is a. e. dyadic (or Butzer and Wagner) differentiate withThe function Kk means the kth Walsh-Kaczmarz function.展开更多
To shed some light on the John-Nirenberg space,the authors of this article introduce the John-Nirenberg-Q space via congruent cubes,JNQp,qα(Rn),which,when p=∞and q=2,coincides with the space Qα(Rn)introduced by Ess...To shed some light on the John-Nirenberg space,the authors of this article introduce the John-Nirenberg-Q space via congruent cubes,JNQp,qα(Rn),which,when p=∞and q=2,coincides with the space Qα(Rn)introduced by Essen,Janson,Peng and Xiao in[Indiana Univ Math J,2000,49(2):575-615].Moreover,the authors show that,for some particular indices,JNQp,qα(Rn)coincides with the congruent John-Nirenberg space,or that the(fractional)Sobolev space is continuously embedded into JNQp,qα(Rn).Furthermore,the authors characterize JNQp,qα(Rn)via mean oscillations,and then use this characterization to study the dyadic counterparts.Also,the authors obtain some properties of composition operators on such spaces.The main novelties of this article are twofold:establishing a general equivalence principle for a kind of’almost increasing’set function that is here introduced,and using the fine geometrical properties of dyadic cubes to properly classify any collection of cubes with pairwise disjoint interiors and equal edge length.展开更多
In this note we show that the general theory of vector valued singular integral operators of Calderón-Zygmund defined on general metric measure spaces,can be applied to obtain Sobolev type regularity properties f...In this note we show that the general theory of vector valued singular integral operators of Calderón-Zygmund defined on general metric measure spaces,can be applied to obtain Sobolev type regularity properties for solutions of the dyadic fractional Laplacian.In doing so,we define partial derivatives in terms of Haar multipliers and dyadic homogeneous singular integral operators.展开更多
文摘A recursive algorithm is adopted for the computation of dyadic Green＇s functions in three-dimensional stratified uniaxial anisotropic media with arbitrary number of layers. Three linear equation groups for computing the coefficients of the Sommerfeld integrals are obtained according to the continuity condition of electric and magnetic fields across the interface between different layers, which are in correspondence with the TM wave produced by a vertical unit electric dipole and the TE or TM wave produced by a horizontal unit electric dipole, respectively. All the linear equation groups can be solved via the recursive algorithm. The dyadic Green＇s functions with source point and field point being in any layer can be conveniently obtained by merely changing the position of the elements within the source term of the linear equation groups. The problem of singularities occurring in the Sommerfeld integrals is efficiently solved by deforming the integration path in the complex plane. The expression of the dyadic Green＇s functions provided by this paper is terse in form and is easy to be programmed, and it does not overflow. Theoretical analysis and numerical examples show the accuracy and effectivity of the algorithm.
基金the Preliminary Research Foundation of National Defense (No,002,2BQ) the Foundation of Fuzhou University (No.0030824649)
文摘Since the Leibniz-Newton formula for derivatives cannot be used in local fields, it is important to investigate the new concept of derivatives in Walsh-analysis, or harmonic analysis on local fields. On the basis of idea of derivatives introduced by Butzer, Schipp and Wade, Weisz has proved that the maximal operators of the one-dimensional dyadic derivative and integral are bounded from the dyadic Hardy space Hp,q to Lp,q, of weak type （L1,L1）, and the corresponding maximal operators of the two-dimensional case are of weak type （Hi, L1）. In this paper, we show that these maximal operators are bounded both on the dyadic Hardy spaces Hp and the hybrid Hardy spaces H^#p 0〈p≤1.
文摘Dyadic coping plays an important role in older adults with mild cognitive impairment and their spouses. Significant correlations were found between dyadic coping and self-efficacy, anxiety and depression, marital quality, and quality of life in elderly patients with mild cognitive impairment and their spouses, and there were gender differences, with a 36.1% [P = 0.028, OR = 0.639, 95% CI (0.429, 0.952)] and 54% [P = 0.004, OR = 0.460, 95% CI (0.269, 0.785)] reduction in the risk of MCI and dementia for older men aged 65 - 69 years with a spouse and for those aged 80 years and older with a spouse, respectively. In contrast, there was no significant difference in the association between having or not having a spouse and developing MCI and dementia in older women (all P > 0.05). Psychosocial interventions, skills interventions, and exercise from the perspective of dyadic relationships were effective in improving the physical and mental health of older adults with mild cognitive impairment and their spouses. However, there is a lack of specific intervention programs for dyadic relationships in the local cultural context as an entry point. Therefore, it is necessary to draw on internal and external relevant literature to treat both partners as a whole for intervention, provide personalized social, cognitive and motor therapy for patients and promote the integration and participation of caregivers, help patients and spouses to improve the sense of well-being and intimacy, reduce the burden of caregivers, and build a dyadic coping intervention program suitable for elderly patients with mild cognitive impairment in China. The current article aims to provide a conceptual review focusing on dyadic coping care to inform the development of a dyadic intervention program suitable for older adults with mild cognitive impairment in China. This review outlines the theoretical concepts, assessment tools, current state of research, and intervention methods for mild cognitive impairment and dyadic coping.
基金Supported by the National Natural Science Founda-tion of China (49984001)
文摘Automatic feature extraction and classification algorithm of echo signal of ground penetrating radar is presented. Dyadic wavelet transform and the average energy of the wavelet coefficients are applied in this paper to decompose and extract feature of the echo signal. Then, the extracted feature vector is fed up to a feed forward muhi layer perceptron classifier. Experimental results based on the measured GPR, echo signals obtained from the Mei shan railway are presented.
基金supported by the Natural Science Foundation of China under Grant Nos.71661001 and 71971190the project of Yunnan Key Laboratory of Smart City and Cyberspace Security under Grant No.202105AG070010。
文摘Micro triadic structure is an important motif and serves the building block of complex networks.In this paper,the authors define structure entropy for a social network and explain this concept by using the coded triads proposed by Davis and Leinhardt in 1972.The proposed structure entropy serves as a new macro-evolution index to measure the network’s stability at a given timestamp.Empirical analysis of real-world network structure entropy discloses rich information on the mechanism that yields given triadic motifs frequency distribution.This paper illustrates the intrinsic link between the micro dyadic/triadic motifs and network structure entropy.Importantly,the authors find that the high proportion of reciprocity and transitivity results in the emergence of hierarchy,order,and cooperation of online social networks.
文摘Homogeneous binary function products are frequently encountered in the sub-universes modeled by databases,spanning from genealogical trees and sports to education and healthcare,etc.Their properties must be discovered and enforced by the software applications managing such data to guarantee plausibility.The(Elementary)Mathematical Data Model provides 17 types of dyadic-based homogeneous binary function product constraint categories.MatBase,an intelligent data and knowledge base management system prototype,allows database designers to simply declare them by only clicking corresponding checkboxes and automatically generates code for enforcing them.This paper describes the algorithms that MatBase uses for enforcing all 17 types of homogeneous binary function product constraint,which may also be employed by developers without access to MatBase.
基金supported by National Natural Science Foundation of China (Grant No. 12171223)the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2021A1515010396)。
文摘Let n≥2 be an integer. We give necessary and sufficient conditions for an integral quadratic form over dyadic local fields to be n-universal by using invariants from Beli's theory of bases of norm generators.Also, we provide a minimal set for testing n-universal quadratic forms over dyadic local fields, as an analogue of Bhargava and Hanke's 290-theorem(or Conway and Schneeberger's 15-theorem) on universal quadratic forms with integer coefficients.
基金Supported by NSFC （Grant Nos. 10671062 and 11071065）, Ph. D Programs Foundation of Ministry Education of China （Grant No. 20094306110004） the first author !Ls also partially supported by the Project-sponsored by SRF for ROCS, SEM, the Fundamental Research Funds for the Central Universities, and China Postdoctoral Science Foundation funded project （Grant No. 20100480942）
文摘The single 2 dilation wavelet multipliers in one-dimensional case and single A-dilation （where A is any expansive matrix with integer entries and [detA[ = 2） wavelet multipliers in twodimen- sional case were completely characterized by Wutam Consortium （1998） and Li Z., et al. （2010）. But there exist no results on multivariate wavelet multipliers corresponding to integer expansive dilation matrix with the absolute value of determinant not 2 in L^2（R^2）. In this paper, we choose 2I2 = （02 20 ） as the dilation matrix and consider the 212-dilation multivariate wavelet ψ = {ψ1, ψ2, ψ3 } （which is called a dyadic bivariate wavelet） multipliers. Here we call a measurable function family f ={fl, f2, f3} a dyadic bivariate wavelet multiplier if ψ1 = （F^-1（f1ψ1）,F^-1（f2ψ2）, F-l（f3ψ3）} is a dyadic bivariate wavelet for any dyadic bivariate wavelet ψ = {ψ1, ψ2, ψ3}, where f and F^- 1 denote the Fourier transform and the inverse transform of function f respectively. We study dyadic bivariate wavelet multipliers, and give some conditions for dyadic bivariate wavelet multipliers. We also give concrete forms of linear phases of dyadic MRA bivariate wavelets.
基金supported by the National Science,Technology and Innovation Plan(NSTIP)Strategic Technologies Programs of the Kingdom of Saudi Arabia under Grant No.08-INF325-02
文摘In this paper, we present a new technique for mammogram enhancement using fast dyadic wavelet transform （FDyWT） based on lifted spline dyadic wavelets and normalized Tsallis entropy. First, a mammogram image is decom- posed into a multiscale hierarchy of low-subband and high-subband images using FDyWT. Then noise is suppressed using normalized Tsallis entropy of the local variance of the modulus of oriented high-subband images. After that, the wavelet coefficients of high-subbands are modified using a non-linear operator and finally the low-subband image at the first scale is modified with power law transformation to suppress background. Though FDyWT is shift-invariant and has better poten- tial for detecting singularities like edges, its performance depends on the choice of dyadic wavclcts. On the other hand, the nulnber of vanishing moments is an important characteristic of dyadic wavelets for singularity analysis because it provides an upper bound measurement for singularity characterization. Using lifting dyadic schemes, we construct lifted spline dyadic wavelets of different degrees with increased number of vanishing moments. We also examine the effect of these wavelets on mammogram enhancement. The method is tested on mammogram images, taken from MIAS （Mammographic Image Analysis Society） database, having various background tissue types and containing different abnormalities. The comparison with tile state-of-the-art contrast enhancement methods reveals that the proposed method performs better and the difference is statistically significant.
基金Supported by the National Natural Science Foundation of China(10671147)
文摘The principles of the new maximal operator H＊ we defined are discussed. We prove that it is bounded from martingale Hardy-Lorentz L^Xp.q[0,1） to the Lorentz L^Xp.q[0,1） for 1/2〈 p〈∞, 0〈~ q ≤ ∞, where X is any Banach space. When the Banach space X has the RN property, the sequence dnHnf converges to f a.e. Meanwhile the convergence in L^Xp norm for 1≤p〈∞ is a consequence of that the family functions K （n∈N） is an approximate identity.
基金supported by the Nation Natural Science Foundation of China(10671147)Wuhan University of Science and Engineering under grant (093877)
文摘In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I＊ and Cesàro mean operator σ＊ are bounded from the B-valued martingale Hardy spaces pΣα, Dα, pLα, p H#α, pKr to Lα （0 α ∞）, respectively. The facts show that it depends on the geometrical properties of the Banach space.
基金the Natural Science Foundation of Education Committee of Anhui Province (No.2001kj198zc).
文摘 In this paper, we construct a class of nowhere differentiable continuous functions by means of the Cantor series expression of real numbers. The constructed functions include some known nondifferentiable functions, such as Bush type functions. These functions are fractal functions since their graphs are in general fractal sets. Under certain conditions, we investigate the fractal dimensions of the graphs of these functions, compute the precise values of Box and Packing dimensions, and evaluate the Hausdorff dimension. Meanwhile, the Holder continuity of such functions is also discussed.
基金Research supported by the Hungarian"M uvel odesi es Kozoktatosi Miniszterium",grant no.FKFP0182/200O,the Bolyai Fellowship of the Hungarian Academy of Science and the Hungarian National Foundation for Scientific Research(OTKA),grant no.M 36511/2001.
文摘The aim of this paper is to prove the following theorem concerning the term by term differentiation the-orem of Walsh-Kaczmarz series. Let (ck) be a decreasing real sequence withare integrable functions and f(x) is a. e. dyadic (or Butzer and Wagner) differentiate withThe function Kk means the kth Walsh-Kaczmarz function.
基金partially supported by the National Natural Science Foundation of China(12122102 and 11871100)the National Key Research and Development Program of China(2020YFA0712900)。
文摘To shed some light on the John-Nirenberg space,the authors of this article introduce the John-Nirenberg-Q space via congruent cubes,JNQp,qα(Rn),which,when p=∞and q=2,coincides with the space Qα(Rn)introduced by Essen,Janson,Peng and Xiao in[Indiana Univ Math J,2000,49(2):575-615].Moreover,the authors show that,for some particular indices,JNQp,qα(Rn)coincides with the congruent John-Nirenberg space,or that the(fractional)Sobolev space is continuously embedded into JNQp,qα(Rn).Furthermore,the authors characterize JNQp,qα(Rn)via mean oscillations,and then use this characterization to study the dyadic counterparts.Also,the authors obtain some properties of composition operators on such spaces.The main novelties of this article are twofold:establishing a general equivalence principle for a kind of’almost increasing’set function that is here introduced,and using the fine geometrical properties of dyadic cubes to properly classify any collection of cubes with pairwise disjoint interiors and equal edge length.
基金supported by the MINCYT in Argentina:CONICET and ANPCyT,UNL and UNComa。
文摘In this note we show that the general theory of vector valued singular integral operators of Calderón-Zygmund defined on general metric measure spaces,can be applied to obtain Sobolev type regularity properties for solutions of the dyadic fractional Laplacian.In doing so,we define partial derivatives in terms of Haar multipliers and dyadic homogeneous singular integral operators.
