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

被引：0
作者：
Liguang Liu
Dachun Yang
机构：
[1] Renmin University of China,Department of Mathematics, School of Information
[2] Beijing Normal University,School of Mathematical Sciences
[3] Laboratory of Mathematics and Complex Systems,undefined
[4] Ministry of Education,undefined
来源：
Chinese Annals of Mathematics, Series B | 2014年 / 35卷
关键词：
Local weight; Triebel-Lizorkin space; Atom; Lusin-Area function; Riesz transform; 46E35; 47B06; 42B20; 42B35;
D O I：
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中图分类号：
学科分类号：
摘要：
In this paper, the authors characterize the inhomogeneous Triebel-Lizorkin spaces Fp,qs,w(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 Fp,qs,w(ℝn are also obtained, which further implies that a (sub)linear operator that maps smooth atoms of Fp,qs,w(ℝn uniformly into a bounded set of a (quasi-)Banach space is extended to a bounded operator on the whole Fp,qs,w(ℝn. As an application, the boundedness of the local Riesz operator on the space Fp,qs,w(ℝn is obtained.
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页码：237 / 260
页数：23
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