The authors give a natural definition of Morrey spaces for Radon measures which may be non-doubling but satisfy certain growth condition, and investigate the boundedness in these spaces of some classical operators in ...The authors give a natural definition of Morrey spaces for Radon measures which may be non-doubling but satisfy certain growth condition, and investigate the boundedness in these spaces of some classical operators in harmonic analysis and their vector-valued extension.展开更多
We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method,...We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method, the ±-method and the Peetre-Gagliardo method, are studied in such a framework. Special emphasis is given to the quasi-Banach case and to the interpolation property.展开更多
In this paper, the author considers the boundedness of strongly singular Calderdn Zygmund operator and commutator generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey ...In this paper, the author considers the boundedness of strongly singular Calderdn Zygmund operator and commutator generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey space. Moreover, the boundedness of strongly singular Calderón- Zygmund operator on the predual of Morrey space is discussed.展开更多
In this paper, we study central BMO estimates for commutators of n-dimensional rough Hardy operators. Furthermore, λ-central BMO estimates for commutators on central Morrey spaces are discussed.
In this note,we characterize the boundedness of the Volterra type operator Tg and its related integral operator Ig on analytic Morrey spaces.Furthermore,the norm and essential norm of those operators are given.As a co...In this note,we characterize the boundedness of the Volterra type operator Tg and its related integral operator Ig on analytic Morrey spaces.Furthermore,the norm and essential norm of those operators are given.As a corollary,we get the compactness of those operators.展开更多
We consider the boundedness of Calderón-Zygmund operators from Hp,}(R^n)(the predual of a Morrey space) to h^p,}(R^n)(the local version of H^p,}). We show that Calderón's commutator is bounded from H^p,}...We consider the boundedness of Calderón-Zygmund operators from Hp,}(R^n)(the predual of a Morrey space) to h^p,}(R^n)(the local version of H^p,}). We show that Calderón's commutator is bounded from H^p,} to h^p,}.展开更多
The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which Mizuhara and Nakai proposed, are equipped with a parameter and a function. Th...The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which Mizuhara and Nakai proposed, are equipped with a parameter and a function. The trace property is one of the main focuses of the present paper, which will clarify the role of the parameter of generalized Morrey spaces. The quarkonial decomposition is obtained as an application of the atomic decomposition. In the end, the relation between the function spaces dealt in the present paper and the foregoing researches is discussed.展开更多
In this paper, the authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey and generalized Morrey spaces, respectively. As their special cases, the corresponding res...In this paper, the authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey and generalized Morrey spaces, respectively. As their special cases, the corresponding results of multilinear Galderón-gygmund operator can be obtained.展开更多
In this paper,the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent generalized weighted Morrey spaces and the variable exponent vanishing generalized w...In this paper,the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent generalized weighted Morrey spaces and the variable exponent vanishing generalized weighted Morrey spaces.And the corresponding commutators generated by BMO function are also considered.展开更多
In this article, the authors establish several equivalent characterizations of fractional Hajlasz-Morrey-Sobolev spaces on spaces of homogeneous type in the sense of Coifman and Weiss.
基金the 21st century COE program at Graduate School of Mathemtical Sciences The University of Tokyo and the sceond author is supported by Fjyukai foundation
文摘The authors give a natural definition of Morrey spaces for Radon measures which may be non-doubling but satisfy certain growth condition, and investigate the boundedness in these spaces of some classical operators in harmonic analysis and their vector-valued extension.
基金supported by National Natural Science Foundation of China(Grant Nos.11471042,11171027 and 11361020)the Alexander von Humboldt Foundation+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120003110003)the Fundamental Research Funds for Central Universities of China(Grant Nos.2013YB60 and 2014KJJCA10)
文摘We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method, the ±-method and the Peetre-Gagliardo method, are studied in such a framework. Special emphasis is given to the quasi-Banach case and to the interpolation property.
基金Supported by the National Natural Science Foundation of China(10571014)the Doctoral Programme Foundation of Institution of Higher Education of China(20040027001)
文摘In this paper, the author considers the boundedness of strongly singular Calderdn Zygmund operator and commutator generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey space. Moreover, the boundedness of strongly singular Calderón- Zygmund operator on the predual of Morrey space is discussed.
基金supported by National Natural Science Foundation of China (GrantNos. 10871024, 10901076)Natural Science Foundation of Shandong Province (Grant No. Q2008A01)+1 种基金supported by National Natural Science Foundation of China (Grant Nos. 10871024, 10931001)supported by the Key Laboratory of Mathematics and Complex System (Beijing Normal University), Ministry of Education,China
文摘In this paper, we study central BMO estimates for commutators of n-dimensional rough Hardy operators. Furthermore, λ-central BMO estimates for commutators on central Morrey spaces are discussed.
基金supported by National Natural Science Foundation of China(Grant Nos.11171203 and 11201280)Research Fund for the Doctoral Program of Higher Education of China(Grant No.20114402120003)National Science Foundation of Guangdong Province(Grant Nos.10151503101000025 and S2011010004511)
文摘In this note,we characterize the boundedness of the Volterra type operator Tg and its related integral operator Ig on analytic Morrey spaces.Furthermore,the norm and essential norm of those operators are given.As a corollary,we get the compactness of those operators.
文摘We consider the boundedness of Calderón-Zygmund operators from Hp,}(R^n)(the predual of a Morrey space) to h^p,}(R^n)(the local version of H^p,}). We show that Calderón's commutator is bounded from H^p,} to h^p,}.
基金Supported by NSFC(No.11571160)Project of Reform and Development Foundation for Local Universities from Central Government of China-Excellent Youth Talent Project of Heilongjiang Province(No.2020YQ07)。
文摘The theory of generalized Besov-Morrey spaces and generalized Triebel-Lizorkin-Morrey spaces is developed. Generalized Morrey spaces, which Mizuhara and Nakai proposed, are equipped with a parameter and a function. The trace property is one of the main focuses of the present paper, which will clarify the role of the parameter of generalized Morrey spaces. The quarkonial decomposition is obtained as an application of the atomic decomposition. In the end, the relation between the function spaces dealt in the present paper and the foregoing researches is discussed.
基金Supported by the the National Natural Science Foundation of China (10571014) the Doctoral Programme Foundation of Institution of Higher Education of China (20040027001).
文摘In this paper, the authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey and generalized Morrey spaces, respectively. As their special cases, the corresponding results of multilinear Galderón-gygmund operator can be obtained.
基金supported by the National Natural Science Foundation of China(No.11561062)Natural Science Foundation of Gansu Province(21JR1RM337).
文摘In this paper,the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent generalized weighted Morrey spaces and the variable exponent vanishing generalized weighted Morrey spaces.And the corresponding commutators generated by BMO function are also considered.
基金supported by the National Natural Science Foundation of China(11471042,11361020 and 11571039)the Specialized Research Fund for the Doctoral Program of Higher Education of China(20120003110003)the Fundamental Research Funds for Central Universities of China(2014KJJCA10)
文摘In this article, the authors establish several equivalent characterizations of fractional Hajlasz-Morrey-Sobolev spaces on spaces of homogeneous type in the sense of Coifman and Weiss.
