Hardy Spaces Associated with Ball Quasi-Banach Function Spaces on Spaces of Homogeneous Type:Littlewood–Paley Characterizations with Applications to Boundedness of Calderón–Zygmund Operators  

作　　者：Xian Jie YAN Zi Yi HE Da Chun YANG Wen YUAN 

机构地区：[1]Laboratory of Mathematics and Complex Systems(Ministry of Education of China),School of Mathematical Sciences,Beijing Normal University,Beijing 100875,P.R.China [2]School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第7期1133-1184,共52页数学学报（英文版）

基　　金：Supported by the National Key Research and Development Program of China(Grant No.2020YFA0712900);the National Natural Science Foundation of China(Grant Nos.11971058,12071197 and 11871100);the Fundamental Research Funds for the Central Universities(Grant Nos.500421359 and 500421126)。

摘　　要：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 space.The 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)^(*)-functions.As 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 new.The 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 

分 类 号：O177.2[理学—数学]