Atomic Decompositions of Triebel-Lizorkin Spaces with Local Weights and Applications  

作　　者：Liguang LIU Dachun YANG 

机构地区：[1]Department of Mathematics,School of Information,Renmin University of China [2]School of Mathematical Sciences,Beijing Normal University,Laboratory of Mathematics and Complex Systems,Ministry of Education

出　　处：《Chinese Annals of Mathematics,Series B》2014年第2期237-260,共24页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.11101425,11171027);the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20120003110003)

摘　　要：Abstract In this paper, the authors characterize the inhomogeneous Triebel-Lizorkin spaces Fs,w p,q （Rn） with local weight w by using the Lusin-area functions for the full ranges of the indices, and then establish their atomic decompositions for s ∈ R, p ∈ （0, 1] and q ∈ [p, ∞）. The novelty is that the weight w here satisfies the classical Muckenhoupt condition only on balls with their radii in （0, 1]. Finite atomic decompositions for smooth functions in Fs,w p,q（Rn） are also obtained, which further implies that a （sub）linear operator that maps smooth atoms of Fs,w p,q（Rn） uniformly into a bounded set of a （quasi-）Banach space is extended to a bounded operator on the whole Fs,w p,q（Rn） As an application, the baundedness of the local Riesz operator on the space Fs,w p,q（Rn） is obtained.

关 键 词：Local weight Triebel-Lizorkin space ATOM Lusin-Area function Riesztransform 

分 类 号：O172.2[理学—数学]