The paper defines an extended Cesaro operator Tg with holomorphic symbol g in the unit ball B of Cn asWhere is the radial derivative of g. In this paper, the author characterizes g for which Tg is bounded (or compact)...The paper defines an extended Cesaro operator Tg with holomorphic symbol g in the unit ball B of Cn asWhere is the radial derivative of g. In this paper, the author characterizes g for which Tg is bounded (or compact) on the Bloch space B and the little Bloch space Bo-展开更多
Both residual Cesaro alpha-integrability （RCI（α） and strongly residual Cesaro alpha- integrability （SRCI（α）） are two special kinds of extensions to uniform integrability, and both asymptotically almost negati...Both residual Cesaro alpha-integrability （RCI（α） and strongly residual Cesaro alpha- integrability （SRCI（α）） are two special kinds of extensions to uniform integrability, and both asymptotically almost negative association （AANA） and asymptotically quadrant sub-independence （AQSI） are two special kinds of dependence structures. By relating the RCI（α） property as well as the SRCI（α） property with dependence condition AANA or AQSI, we formulate some tail-integrability conditions under which for appropriate α the RCI（（α） property yields Ll-convergence results and the SRCI（α） property yields strong laws of large numbers, which is the continuation of the corresponding literature.展开更多
In this article, we characterize the boundedness and compactness of extended Cesaro operators on the spaces BMOA by the Carleson measures in the unit ball. Mea while, we study the pointwise multipliers on BMOA.
In this article we introduce the difference sequence spaces Wo [f, △m], W1 [f, △m],W∞[f ,△m] and S[f, △m], defined by a modulus function f. We obtain a relation between W1 【f, △m] ∩ l∞[f, △m] and S[f, △m]...In this article we introduce the difference sequence spaces Wo [f, △m], W1 [f, △m],W∞[f ,△m] and S[f, △m], defined by a modulus function f. We obtain a relation between W1 【f, △m] ∩ l∞[f, △m] and S[f, △m]∩ l∞[f, △m] and prove some inclusion results.展开更多
Let S^(d-1) = {x : |x| = 1} be a unit sphere of the d-dimensional Euclideanspace R^d and let H^p = H^p(S^(d-1)) (0 < p ≤ 1) denote the real Hardy space on S^(d-1). For 0 < p≤ 1 and f ∈ H^p(S^(d-1)), let E_j (...Let S^(d-1) = {x : |x| = 1} be a unit sphere of the d-dimensional Euclideanspace R^d and let H^p = H^p(S^(d-1)) (0 < p ≤ 1) denote the real Hardy space on S^(d-1). For 0 < p≤ 1 and f ∈ H^p(S^(d-1)), let E_j (f, H^p) (j =0,1,...) be the best approximation of f byspherical polynomials of degree less than or equal to j, in the space H^p(S^(d-1)). Given adistribution f on S^(d-1), its Cesaro mean of order δ > -1 is denoted by σ_k~δ(f). For 0 < p ≤1, it is known that δ(p) := (d-1)/p - d/2 is the critical index for the uniform summability ofσ_k~δ(f) in the metric H^p.展开更多
Let B be the unit ball of a complex Banach space X. In this paper, we generalize the Bloch-type spaces and the little Bloch-type spaces to the open unit ball B by using the radial derivative. Next, we de?ne an extende...Let B be the unit ball of a complex Banach space X. In this paper, we generalize the Bloch-type spaces and the little Bloch-type spaces to the open unit ball B by using the radial derivative. Next, we de?ne an extended Ces`aro operator T_φ with the holomorphic symbol φ and characterize those φ for which T_φ is bounded between the Bloch-type spaces and the little Bloch-type spaces. We also characterize those φ for which T_φ is compact between the Bloch-type spaces and the little Bloch-type spaces under some additional assumption on the symbol φ. When B is the open unit ball of a ?nite dimensional complex Banach space X, this additional assumption is automatically satis?ed.展开更多
In this article, we introduce the concept of lacunary statistical convergence of order a of real number sequences and give some inclusion relations between the sets of lacu- nary statistical convergence of order α an...In this article, we introduce the concept of lacunary statistical convergence of order a of real number sequences and give some inclusion relations between the sets of lacu- nary statistical convergence of order α and strong Nα （p）-summability. Furthermore, some relations between the spaces Nθα （p） and Sθα are examined.展开更多
This paper deals with the convergence of the Cesaro mean for the rational orthonormal bases. Provided the set of zeroes of rational orthonormal bases is formed by a periodic repetition of the same finite sequence, the...This paper deals with the convergence of the Cesaro mean for the rational orthonormal bases. Provided the set of zeroes of rational orthonormal bases is formed by a periodic repetition of the same finite sequence, the explicit expression of so-called block-Fejer kernel is available, and some properties of the block-Fejer kernel are discussed. Based on the convergence of the block-Cesaro mean, the convergence of Cesaro mean is also provided.展开更多
In this article we show that the order of the point value, in the sense of Lojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming ...In this article we show that the order of the point value, in the sense of Lojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming that the order of the point values and certain order of growth at infinity are given for a tempered distribution, we estimate the order of summability of the Fourier inversion formula. For Fourier series, and in other cases, it is shown that if the distribution has a distributional point value of order k, then its Fourier series is e.v. Cesaro summable to the distributional point value of order k＋1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. Cesaro summable of order k, then the distribution is the （k ＋ 1）-th derivative of a locally integrable function, and the distribution has a distributional point value of order k ＋ 2. We also establish connections between orders of summability and local behavior for other Fourier inversion problems.展开更多
In this paper,we obtain the characterizations on μ for（p,q）-φCarleson measure,and discuss the boundedness（and compactness） of the extended Cesaro operators T g between different weighted Bergman spaces as some a...In this paper,we obtain the characterizations on μ for（p,q）-φCarleson measure,and discuss the boundedness（and compactness） of the extended Cesaro operators T g between different weighted Bergman spaces as some application.展开更多
In this paper, we prove the （L^p, L^q）-boundedness of （fractional） Hausdorff operators with power weight on Euclidean spaces. As special cases, we can obtain some well known results about Hardy operators.
In the present paper, a new difference matrix via difference operator D is introduced. Let x = （xk） be a sequence of real numbers, then the difference operatorD is defined by D（x）n =∑kn=0（-1）k（n-kn）xk,where ...In the present paper, a new difference matrix via difference operator D is introduced. Let x = （xk） be a sequence of real numbers, then the difference operatorD is defined by D（x）n =∑kn=0（-1）k（n-kn）xk,where n = 0,1,2,3,.... Several interestingproperties of the new operator D are discussed.展开更多
In this article, the Banach space X and the martingales with values in it are considered. It is shown that the maximal operators of the one-dimensional dyadic derivative of the dyadic integral and Cesaro means are bou...In this article, the Banach space X and the martingales with values in it are considered. It is shown that the maximal operators of the one-dimensional dyadic derivative of the dyadic integral and Cesaro means are bounded from the dyadic Hardy- Lorentz space pH^-ra（X） to Lra（X） when X is isomorphic to a p-uniformly smooth space （1 〈p ≤ 2）. And it is also bounded from Hra（X） to Lra（X） （0 〈 r 〈 ∞,0 〈 a≤oc） when X has Radon-Nikodym property. In addition, some weak-type inequalities are given.展开更多
The Bloch-type space Bω consists of all functions f ∈ H（B） for which｜｜f｜｜Bω =sup z∈Bω（z）｜△f（z）｜〈∞Let Tφ be the extended Cesaro operator with holomorphic symbol φ. The essential norm of Tφ as an ...The Bloch-type space Bω consists of all functions f ∈ H（B） for which｜｜f｜｜Bω =sup z∈Bω（z）｜△f（z）｜〈∞Let Tφ be the extended Cesaro operator with holomorphic symbol φ. The essential norm of Tφ as an operator from Bω to Bμ is denoted by ｜｜Tφ｜｜e,Bω→Bμ. The purpose of this paper is to prove that, for w, ω normal and φ ∈ H（B）｜｜Tφ｜｜e,Bω→Bμ≈lim sup｜z｜→1μ（z）｜Rφ（z）｜∫0^｜z｜dt/ω（t）.展开更多
Let μ, v ∈ [0, 1） be normal functions and g be holomorphic function on the unit ball. In this paper, we prove that the generalized Cesaro operator Tg ：βμ→βv is bounded and compact.
We characterize the symbol for which the induced extended Cesàro operator T: Bω→ Bμ(respectively, Bω,0 → Bμ,0) is bounded or compact, where is a given holomorphic function on the unit disc D, ω and...We characterize the symbol for which the induced extended Cesàro operator T: Bω→ Bμ(respectively, Bω,0 → Bμ,0) is bounded or compact, where is a given holomorphic function on the unit disc D, ω and μ both are normal functions on [0,1).展开更多
基金This research is partially supported by the 151 Projectionthe Natural Science Foundation of Zhejiang Province.
文摘The paper defines an extended Cesaro operator Tg with holomorphic symbol g in the unit ball B of Cn asWhere is the radial derivative of g. In this paper, the author characterizes g for which Tg is bounded (or compact) on the Bloch space B and the little Bloch space Bo-
基金Supported by National Natural Science Foundation of China (Grant No. 10871217)Natural Science Foundation Project of CQ CSTC of China (Grant No. 2009BB2370)SCR of Chongqing Municipal Education Commission (Grant Nos. KJ090703, KJ100726)
文摘Both residual Cesaro alpha-integrability （RCI（α） and strongly residual Cesaro alpha- integrability （SRCI（α）） are two special kinds of extensions to uniform integrability, and both asymptotically almost negative association （AANA） and asymptotically quadrant sub-independence （AQSI） are two special kinds of dependence structures. By relating the RCI（α） property as well as the SRCI（α） property with dependence condition AANA or AQSI, we formulate some tail-integrability conditions under which for appropriate α the RCI（（α） property yields Ll-convergence results and the SRCI（α） property yields strong laws of large numbers, which is the continuation of the corresponding literature.
基金supported by the National Natural Science Foundation of China(10771064,11101139)Natural Science Foundation of Zhejiang province (Y7080197,Y6090036,Y6100219)Foundation of Creative Group in Universities of Zhejiang Province (T200924)
文摘In this article, we characterize the boundedness and compactness of extended Cesaro operators on the spaces BMOA by the Carleson measures in the unit ball. Mea while, we study the pointwise multipliers on BMOA.
文摘In this article we introduce the difference sequence spaces Wo [f, △m], W1 [f, △m],W∞[f ,△m] and S[f, △m], defined by a modulus function f. We obtain a relation between W1 【f, △m] ∩ l∞[f, △m] and S[f, △m]∩ l∞[f, △m] and prove some inclusion results.
基金The authors are partially supported by NNSF of China under the grant#10071007
文摘Let S^(d-1) = {x : |x| = 1} be a unit sphere of the d-dimensional Euclideanspace R^d and let H^p = H^p(S^(d-1)) (0 < p ≤ 1) denote the real Hardy space on S^(d-1). For 0 < p≤ 1 and f ∈ H^p(S^(d-1)), let E_j (f, H^p) (j =0,1,...) be the best approximation of f byspherical polynomials of degree less than or equal to j, in the space H^p(S^(d-1)). Given adistribution f on S^(d-1), its Cesaro mean of order δ > -1 is denoted by σ_k~δ(f). For 0 < p ≤1, it is known that δ(p) := (d-1)/p - d/2 is the critical index for the uniform summability ofσ_k~δ(f) in the metric H^p.
基金supported by Japan Society for the Promotion of Science KAKENHI (Grant No. JP16K05217)
文摘Let B be the unit ball of a complex Banach space X. In this paper, we generalize the Bloch-type spaces and the little Bloch-type spaces to the open unit ball B by using the radial derivative. Next, we de?ne an extended Ces`aro operator T_φ with the holomorphic symbol φ and characterize those φ for which T_φ is bounded between the Bloch-type spaces and the little Bloch-type spaces. We also characterize those φ for which T_φ is compact between the Bloch-type spaces and the little Bloch-type spaces under some additional assumption on the symbol φ. When B is the open unit ball of a ?nite dimensional complex Banach space X, this additional assumption is automatically satis?ed.
文摘In this article, we introduce the concept of lacunary statistical convergence of order a of real number sequences and give some inclusion relations between the sets of lacu- nary statistical convergence of order α and strong Nα （p）-summability. Furthermore, some relations between the spaces Nθα （p） and Sθα are examined.
基金Supported in part by NSFC under Grant 10771053, by the National Research Foundation for the Doctoral Program of Higher Education of China （SRFDP） under Grant 20060512001, and by Natural Science Foundation of Hubei Province under Grant 2007ABA139
文摘This paper deals with the convergence of the Cesaro mean for the rational orthonormal bases. Provided the set of zeroes of rational orthonormal bases is formed by a periodic repetition of the same finite sequence, the explicit expression of so-called block-Fejer kernel is available, and some properties of the block-Fejer kernel are discussed. Based on the convergence of the block-Cesaro mean, the convergence of Cesaro mean is also provided.
基金support by the Louisiana State Board of Regents grant LEQSF(2005-2007)-ENH-TR-21
文摘In this article we show that the order of the point value, in the sense of Lojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming that the order of the point values and certain order of growth at infinity are given for a tempered distribution, we estimate the order of summability of the Fourier inversion formula. For Fourier series, and in other cases, it is shown that if the distribution has a distributional point value of order k, then its Fourier series is e.v. Cesaro summable to the distributional point value of order k＋1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. Cesaro summable of order k, then the distribution is the （k ＋ 1）-th derivative of a locally integrable function, and the distribution has a distributional point value of order k ＋ 2. We also establish connections between orders of summability and local behavior for other Fourier inversion problems.
基金Supported by the National Natural Science Foundation of China (Grant No. 10771064)the Natural Science Foundation of Zhejiang Province (Grant Nos. Y7080197+2 种基金 Y6090036 Y6100219)Foundation of Creative Group in Universities of Zhejiang Province (Grant No. T200924)
文摘In this paper,we obtain the characterizations on μ for（p,q）-φCarleson measure,and discuss the boundedness（and compactness） of the extended Cesaro operators T g between different weighted Bergman spaces as some application.
基金supported by Research Foundation of Hangzhou Dianzi University(No.KYS075614051)PRSF of Zhejiang(No.BSH1302046)NSFC(No.11271330)
文摘In this paper, we prove the （L^p, L^q）-boundedness of （fractional） Hausdorff operators with power weight on Euclidean spaces. As special cases, we can obtain some well known results about Hardy operators.
文摘In the present paper, a new difference matrix via difference operator D is introduced. Let x = （xk） be a sequence of real numbers, then the difference operatorD is defined by D（x）n =∑kn=0（-1）k（n-kn）xk,where n = 0,1,2,3,.... Several interestingproperties of the new operator D are discussed.
基金supported by the National Natural Science Foundation of China (10371093)
文摘In this article, the Banach space X and the martingales with values in it are considered. It is shown that the maximal operators of the one-dimensional dyadic derivative of the dyadic integral and Cesaro means are bounded from the dyadic Hardy- Lorentz space pH^-ra（X） to Lra（X） when X is isomorphic to a p-uniformly smooth space （1 〈p ≤ 2）. And it is also bounded from Hra（X） to Lra（X） （0 〈 r 〈 ∞,0 〈 a≤oc） when X has Radon-Nikodym property. In addition, some weak-type inequalities are given.
基金Supported by the NNSF of China（10771064） Supported by the Natural Science Foundation of Zhejiang Province（YT080197, Y6090036, Y6100219） Supported by the Foundation of Creative Group in Colleges and Universities of Zhejiang Province（T200924） Acknowledgement The author would like to express her thanks to her supervisor, Prof HU Zhang-jian, for his guidance.
文摘The Bloch-type space Bω consists of all functions f ∈ H（B） for which｜｜f｜｜Bω =sup z∈Bω（z）｜△f（z）｜〈∞Let Tφ be the extended Cesaro operator with holomorphic symbol φ. The essential norm of Tφ as an operator from Bω to Bμ is denoted by ｜｜Tφ｜｜e,Bω→Bμ. The purpose of this paper is to prove that, for w, ω normal and φ ∈ H（B）｜｜Tφ｜｜e,Bω→Bμ≈lim sup｜z｜→1μ（z）｜Rφ（z）｜∫0^｜z｜dt/ω（t）.
基金Foundation item： the Natural Science Foundation of the Education Commission of Jiangsu Province （No. 07KJBll0115）.
文摘Let μ, v ∈ [0, 1） be normal functions and g be holomorphic function on the unit ball. In this paper, we prove that the generalized Cesaro operator Tg ：βμ→βv is bounded and compact.
基金Supported by the National Natural Science Foundation of China(10471039)Supported by the Natural Science Foundation of Zhejiang Province(Y606197)Supported by the Foundation of Education of Zhejiang Province(20070482)
文摘We characterize the symbol for which the induced extended Cesàro operator T: Bω→ Bμ(respectively, Bω,0 → Bμ,0) is bounded or compact, where is a given holomorphic function on the unit disc D, ω and μ both are normal functions on [0,1).
