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Acta Mathematica Sinica,English Series 2022年第7期38卷 1133-1184页

作者： Xian Jie YAN Zi Yi HE Da Chun YANG Wen YUAN Laboratory of Mathematics and Complex Systems(Ministry of Education of China) School of Mathematical SciencesBeijing Normal UniversityBeijing 100875P.R.China School of Science Beijing University of Posts and TelecommunicationsBeijing 100876P.R.China

Let(X,ρ,μ)be a space of homogeneous type in the sense of Coifman and Weiss,and Y(X)a ball quasi-Banach function space on X,which supports both a Fefferman–Stein vector-valued maximal inequality and the boundedness of the powered Hardy–littlewood maximal operator on its associate *** authors first introduce the Hardy space H_(Y)(X)associated with Y(X),via the Lusin-area function,and then establish its various equivalent characterizations,respectively,in terms of atoms,molecules,and littlewood–paley g-functions and g_(λ)^(*)-*** an application,the authors obtain the boundedness of Calderón–Zygmund operators from H_(Y)(X)to Y(X),or to H_(Y)(X)via first establishing a boundedness criterion of linear operators on H_(Y)(X).All these results have a wide range of generality and,particularly,even when they are applied to variable Hardy spaces,the obtained results are also *** major novelties of this article exist in that,to escape the reverse doubling condition ofμand the triangle inequality ofρ,the authors subtly use the wavelet reproducing formula,originally establish an admissible molecular characterization of H_(Y)(X),and fully apply the geometrical properties of X expressed by dyadic reference points or dyadic cubes.

关键词： ball quasi-Banach function space Hardy space space of homogeneous type littlewood-paley function Calderón-Zygmund operator

BMO Boundedness of Generalized littlewood-paleyfunctions

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Journal of Mathematical Research and Exposition 2002年第4期22卷 515-518页

作者：李文明河北师范大学数信学院河北石家庄050016

It is proved that the image of a BMO function under the generalized littlewood-paley functions is either equal to infinity almost everywhere or in BMO.

关键词： littlewood-paley function BMO.

littlewood-paley and Pseudo-Differential Operators on Herz-type Spaces over Vilenkin Groups

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Acta Mathematica Sinica,English Series 2004年第5期20卷 779-784页

作者： YuePingZHU DepartmentofMathematics NantongUniversityNantong226007P.R.China

In this paper,we mainly investigate the boundedness of littlewood-paley functions and pseudo-differential operators on weighted Herz-type Hardy spaces over locally compact Vilenkin groups.

关键词： Vilenkin groups Herz-type Hardy spaces littlewood-paley function

littlewood-paley CHARACTERIZATIONS OF ANISOTROPIC HARDY-LORENTZ SPACES

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Acta Mathematica Scientia 2018年第1期38卷 1-33页

作者：刘军杨大春袁文 Laboratory of Mathematics and Complex Systems School of Mathematical SciencesBeijing Normal UniversityBeijing 100875China

Let p∈（0, 1], q∈（0, ∞] and A be a general expansive matrix on Rn. Let HAp,q （Rn） be the anisotropic Hardy-Lorentz spaces associated with A defined via the non-tangential grand maximal function. In this article, the authors characterize HAp,q（Rn） in terms of the Lusin-area function, the littlewood-paley g-function or the littlewood-paley gλ＊-function via first establishing an anisotropic Fefferman-Stein vector-valued inequality in the Lorentz space Lp,q（Rn）. All these characterizations are new even for the classical isotropic Hardy-Lorentz spaces on Rn. Moreover, the range of λ in the gλ＊-function characterization of HAp,q （Rn） coincides with the best known one in the classical Hardy space Hp（Rn） or in the anisotropic Hardy space HAp （Rn）.

关键词： Lorentz space anisotropic Hardy-Lorentz space expansive matrix Calderón reproducing formula littlewood-paley function

Characterizations of product Hardy space associated to Schrodinger operators

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Applied Mathematics(A Journal of Chinese Universities) 2019年第4期34卷 379-392页

作者： ZHAO Kai LIU Su-ying JIANG Xiu-tian School of Mathematics and Statistics Qingdao University

Let L1 and L2 be the Schrodinger operators on Rn and Rm, respectively. By using different maximal functions and littlewood-paley g function on distinct variables, in this paper,some characterizations for functions in ... 详细信息

关键词： Product Hardy space Schrodinger operator characterization littlewood-paley function maximal function

Maximal function characterizations of Hardy spaces on RD-spaces and their applications

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Science China Mathematics 2008年第12期51卷 2253-2284页

作者： Loukas GRAFAKOS Department of Mathematics University of Missouri

Let X be an RD-space, i.e., a space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property. Assume that X has a “dimension” n. For α ∈ (0, ∞) denote by H α p (X), H d p (X), and H *,p (X) the corresponding Hardy spaces on X defined by the nontangential maximal function, the dyadic maximal function and the grand maximal function, respectively. Using a new inhomogeneous Calderón reproducing formula, it is shown that all these Hardy spaces coincide with L p (X) when p ∈ (1,∞] and with each other when p ∈ (n/(n + 1), 1]. An atomic characterization for H ?,p (X) with p ∈ (n/(n + 1), 1] is also established; moreover, in the range p ∈ (n/(n + 1),1], it is proved that the space H *,p (X), the Hardy space H p (X) defined via the littlewood-paley function, and the atomic Hardy space of Coifman andWeiss coincide. Furthermore, it is proved that a sublinear operator T uniquely extends to a bounded sublinear operator from H p (X) to some quasi-Banach space B if and only if T maps all (p, q)-atoms when q ∈ (p, ∞)∩[1, ∞) or continuous (p, ∞)-atoms into uniformly bounded elements of B.

关键词： space of homogeneous type Calderón reproducing formula space of test function maximal function Hardy space atom littlewood-paley function sublinear operator quasi-Banach space 42B25 42B30 47B38 47A30