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atomic decomposition FOR B-VALUED R.V. SEQUENCE SPACES

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Acta Mathematica Scientia 2009年第1期29卷 151-159页

作者：李驭繁刘培德 Department of Mathematics Wuhan University

In this article,atomic decompositions and the duals of some B-valued ***- quence spaces are *** results show that it closely depends on the geometrical properties of the sequence that take values in.

关键词： atomic decomposition B-valued r.v.sequence space dual geometry of Banach space

atomic decomposition characterizations of weighted multiparameter Hardy spaces

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Frontiers of Mathematics in China 2012年第6期7卷 1195-1212页

作者： Xinfeng WU Department of Mathematics China University of Mining and Technology (Beijing)Beijing 100083 China

Let w E Am. In this paper, we introduce weighted-（p,q） atomicHardy spaces Hwp,q（Rn × Rm） for 0 〈 p ≤ 1, q 〉 qw and show that the weighted Hardy space Hwp（Rn × Rm） defined via Littlewood-Paley square functions coincides with Hwp,q（Rn × Rm） for 0 〈 p ≤ 1, q 〉 qw. As applications, we get a general principle on the Hwp（Rn × Rm to Lwp（Rn × Rm） boundedness and a boundedness criterion for two parameter singular integrals on the weighted Hardy spaces.

关键词： atomic decomposition multiparameter Hardy spaces A∞ weight

atomic decomposition and Boundedness Criterion of Operators on Multi-parameter Hardy Spaces of Homogeneous Type

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Acta Mathematica Sinica,English Series 2012年第7期28卷 1329-1346页

作者： Guo Zhen LU Ya Yuan XIAO Department of Mathematics Wayne State University

The main purpose of this paper is to derive a new （p,q）-atomic decomposition on the multi-parameter Hardy space HP（X1 × X2） for 0 〈 po 〈 P ≤ 1 for some po and all 1 〈 q 〈 ∞, where X1 ×X2 is the product of two spaces of homogeneous type in the sense of Coifman and Weiss. This decomposition converges in both L^q（X1 × X2）（for 1 〈 q 〈 ∞） and Hardy space HP（X1× X2）（for 0 〈 p _〈 1）. As an application, we prove that an operator T, which is bounded on Lq（X1× X2） for some 1 〈 q 〈 ∞, is bounded from H^p（X1 × X2） to L^p（X1 × X2） if and only if T is bounded uniformly on all （p, q）-product atoms in LP（X1 × X2）. The similar boundedness criterion from HP（X1 × X2） to HP（X1 × X2） is also obtained.

关键词： atomic decomposition boundedness criterion spaces of homogeneous type multi- parameter Hardy spaces CalderSn's reproducing formula Littlewood Paley theory Journ's covering lemma

Finite atomic decomposition Characterization of Variable Anisotropic Hardy Spaces

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Acta Mathematica Sinica,English Series 2022年第3期38卷 571-590页

作者： An Kang YU Ya Juan YANG Bao De LI Ai Ting WANG College of Mathematics and System Science Xinjiang UniversityUrumqi830046P.R.China School of Mathematics and Statistics Qinhai Nationalities UniversityXining810007P.R.China

In 2011,Dekel et *** highly geometric Hardy spaces H^(p)(Θ),for the full range 0 详细信息

In 2011,Dekel et *** highly geometric Hardy spaces H^(p)(Θ),for the full range 0atomic decomposition characterization of Hardy spaces H^(p)(Θ)and as an application,the authors prove that given an admissible triplet(p,q,l)with 1≤q≤∞,if T is a sublinear operator and uniformly bounded elements of some quasi-Banach space B for maps all(p,q,l)-atoms with q<∞(or all continuous(p,q,l)-atoms with q=∞),then T uniquely extends to a bounded sublinear operator from H^(p)(Θ)to *** results generalize the known results on the anisotropic Hardy spaces of Bownik et al.

关键词： Anisotropy Hardy space atomic decomposition sublinear operator

THE BOUNDEDNESS OF OPERATORS ON WEIGHTED MULTI-PARAMETER LOCAL HARDY SPACES

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Acta Mathematica Scientia 2024年第1期44卷 386-404页

作者：丁卫汤彦朱月萍 School of Sciences Nantong UniversityNantong226007China Department of Mathematics Nantong Normal CollegeNantong226010China

Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality *** this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.

关键词： weighted multi-parameter local Hardy spaces atomic decomposition boundedness inhomogeneous Journéclass

atomic decompositions of Weak Hardy Spaces of B-Valued Martingales

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Wuhan University Journal of Natural Sciences 2006年第3期11卷 456-460页

作者： MA Tao LIU Peide School of Mathematics and Statistics Wuhan UniversityWuhan 430072 Hubei China

The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0〈r≤1. Here the results are connected closely with the p-uniform smoothness and q-uniform convexity of Banach spaces which the martingales take values in.

关键词： atomic decomposition weak Hardy space B-valued martingale

B-valued martingale spaces with small index and atomic decompositions

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Science China Mathematics 2001年第11期44卷 1361-1372页

作者：刘培德于林 1. College of Mathematics and Computer Sciences Wuhan University 430072 Wuhan China

Some atomic decomposition theorems for Banach-space-valued martingales are established. Using them, the embedding relationships between martingale spaces with small index are discussed. The results obtained here are connected closely with the p-uniform smoothness and q-uniform convexity of Banach space in which the martingales take values.

关键词： Banach-space-valued martingale atomic decomposition martingale space geometry of Banaeh space

WEAK atomic decompositionS OF MARTINGALE HARDY-LORENTZ SPACES AND APPLICATIONS

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Acta Mathematica Scientia 2012年第3期32卷 1157-1166页

作者：任颜波郭铁信 School of Mathematics and Systems Science Beihang University School of Mathematics and Statistics Henan University of Scinence and Technology

In this article, we establish some atomic decomposition theorems for martin- gale Hardy-Lorentz spaces. As applications, with the help of weak atomic decompositions, some interpolation theorems for martingale Hardy-Lo... 详细信息

关键词： Martingale Hardy-Lorentz space weak atom atomic decomposition inter- polation

atomic DECOatomic decompositionS AND DUALS OF WEAK HARDY SPACES OF B-VALUED MARTINGALES

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Acta Mathematica Scientia 2009年第5期29卷 1439-1452页

作者：马涛刘培德 School of Mathematics and Statistics Wuhan University

In this article, several weak Hardy spaces of Banach-space-valued martingales are introduced, some atomic decomposition theorems for them are established and their duals are investigated. The results closely depend on... 详细信息

关键词： martingale atomic decomposition weak Hardy space geometry of Banach space