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Weighted Estimates for Marcinkiewicz Integrals with Non-Doubling Measures 认领 引用 被引量：6
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作者 Songbai WANG Yinsheng JIANG Baode LI 《Journal of Mathematical Research with Applications》 CSCD 2012年第2期223-234,共12页
Le be a nonnegative Radon measure on Rd which satisfies the growth condition （B（x, r）） Cotfor all x E Rd and r 〉 O, where Co is a fixed constant and 0 〈 n d. The purpose of this paper is to establish the bounded... Le be a nonnegative Radon measure on Rd which satisfies the growth condition （B（x, r）） Cotfor all x E Rd and r 〉 O, where Co is a fixed constant and 0 〈 n d. The purpose of this paper is to establish the boundedness of the Marcinkiewicz integrals from LP（u） to LP（u）, where u is a weight function of Muckenhoupt type associated with ~. 展开更多
关键词 maximal singular integrals Muckenhoupt type weights sharp maximal operators non-doubling measures.
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BOUNDEDNESS OF VECTOR-VALUED CALDERN-ZYGMUND OPERATORS ON HERZ SPACES WITH NON-DOUBLING MEASURES 认领 引用
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作者 Baode Li Yinsheng Jiang Hui Cao 《Analysis in Theory and Applications》 2007年第2期138-146,共9页
In the paper we obtain vector-valued inequalities for Calderon-Zygmund operator, simply CZO on Herz space and weak Herz space. In particular, we obtain vector-valued inequalities for CZO on L^q（R^d,｜x｜^α d μ）spa... In the paper we obtain vector-valued inequalities for Calderon-Zygmund operator, simply CZO on Herz space and weak Herz space. In particular, we obtain vector-valued inequalities for CZO on L^q（R^d,｜x｜^α d μ）space, with 1〈q〈∞,-n〈α〈n（q-1）,and on L^1,∞ （R^d,｜x｜^α d μ）space,with -n〈α〈0. 展开更多
关键词 Herz space weak Herz space non-doubling measure,Calderon-Zygmund operator
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THE BOUNDEDNESS FOR COMMUTATORS OF ANISOTROPIC CALDERóN-ZYGMUND OPERATORS 认领 引用 被引量：1
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作者 Jinxia LI Baode LI Jianxun HE 《Acta Mathematica Scientia》 SCIE CSCD 2020年第1期45-58,共14页
Let T be an anisotropic Calderón-Zygmund operator andφ:R^n×[0,∞)→[0,∞)be an anisotropic Musielak-Orlicz function withφ(x,·)being an Orlicz function andφ(·,t)being a Muckenhoupt A∞(A)weight.I... Let T be an anisotropic Calderón-Zygmund operator andφ:R^n×[0,∞)→[0,∞)be an anisotropic Musielak-Orlicz function withφ(x,·)being an Orlicz function andφ(·,t)being a Muckenhoupt A∞(A)weight.In this paper,our goal is to study two boundedness theorems for commutators of anisotropic Calderon-Zygmund operators.Precisely,when b∈BMOw(R^n,A)(a proper subspace of anisotropic bounded mean oscillation space BMO(R^n,A)),the commutator[b,T]is bounded from anisotropic weighted Hardy space H^1ω(R^n,A)to weighted Lebesgue space L^1ω(R^n)and when b∈BMO(R^n)(bounded mean oscillation space),the commutator[b,T]is bounded on Musielak-Orlicz space L^φ(R^n),which are extensions of the isotropic setting. 展开更多
关键词 expansive dilation Muckenhoupt weight weighted Hardy space Calderón-Zygmund operator commutator
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Anisotropic weak Hardy spaces of Musielak- Orlicz type and their applications 认领 引用
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作者 Hui ZHANG Chunyan QI Baode LI 《Frontiers of Mathematics in China》 SCIE CSCD 2017年第4期993-1022,共30页
Anisotropy is a common attribute of the nature, which shows different characterizations in different directions of all or part of the physical or chemical properties of an object. The anisotropic property, in mathemat... Anisotropy is a common attribute of the nature, which shows different characterizations in different directions of all or part of the physical or chemical properties of an object. The anisotropic property, in mathematics,can be expressed by a fairly general discrete group of dilations where A is a real matrix with all its elgenvalues A satisfy . The aim of this article is to study a general class of anisotropic function spaces, some properties and applications of these spaces. Let be an anisotropic p-growth function with . The purpose of this article is to find an appropriate general space which includes weak Hardy space of Fefferman and Soria, weighted weak Hardy space of Quek and Yang, and anisotropic weak Hardy space of Ding and Lan. For this reason, we introduce the anisotropic weak Hardy space of Musielak-Orlicz type and obtain its atomic characterization. As applications, we further obtain an interpolation theorem adapted to and the boundedness of the anisotropic Calder6n-Zygmund operator from. It is worth mentioning that the superposition principle adapted to the weak Musielak-Orlicz function space, which is an extension of a result of E. M. Stein, M. Taibleson and G. Weiss, plays an important role in the proofs of the atomic decomposition of and the interpolation theorem. 展开更多
关键词 Expansive dilation Muckenhoupt weight weak Hardy space,Musielak-Orlicz function atomic decomposition Calderdn-Zygmund operator
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