Atomic decompositions of Triebel-Lizorkin spaces with local weights and applications

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• 作者：Liguang Liu (1)
  Dachun Yang (2)
  
• 关键词：Local weight ; Triebel ; Lizorkin space ; Atom ; Lusin ; Area function ; Riesz transform ; 46E35 ; 47B06 ; 42B20 ; 42B35
• 刊名：Chinese Annals of Mathematics - Series B
• 出版年：2014
• 出版时间：March 2014
• 年：2014
• 卷：35
• 期：2
• 页码：237-260
• 全文大小：375 KB
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• 作者单位：Liguang Liu (1)
  Dachun Yang (2)
  
  1. Department of Mathematics, School of Information, Renmin University of China, Beijing, 100872, China
  2. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, China
  
• ISSN：1860-6261

文摘

In this paper, the authors characterize the inhomogeneous Triebel-Lizorkin spaces F p,q s,w (?sup class="a-plus-plus"> n 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 ?? 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 F p,q s,w (?sup class="a-plus-plus"> n are also obtained, which further implies that a (sub)linear operator that maps smooth atoms of F p,q s,w (?sup class="a-plus-plus"> n uniformly into a bounded set of a (quasi-)Banach space is extended to a bounded operator on the whole F p,q s,w (?sup class="a-plus-plus"> n . As an application, the boundedness of the local Riesz operator on the space F p,q s,w (?sup class="a-plus-plus"> n is obtained.