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：
暂无
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.
引用
收藏
页码：237 / 260
页数：23
相关论文
共 42 条
[11]  
Frazier M(2011)Entropy and approximation numbers of embeddings of function spaces with muckenhoupt weights, II. general weights Ann. Acad. Sci. Fenn. Math. 36 111-138
[12]  
Jawerth B(2011)Entropy numbers of embeddings of function spaces with muckenhoupt weights, III. Some limiting cases J. Funct. Spaces Appl. 9 129-178
[13]  
Goldberg D(2009)Wavelet bases in the weighted Besov and Triebel-Lizorkin spaces with J. Approx. Theory 161 656-673
[14]  
Han Y(2012)-weights Math. Nachr. 285 103-126
[15]  
Paluszyński M(2009)Atomic decomposition for weighted Besov and Triebel-Lizorkin spaces Studia Math. 190 163-183
[16]  
Weiss G(2001)Boundedness of sublinear operators in Triebel-Lizorkin spaces via atoms Math. Nachr. 224 145-180
[17]  
Haroske D D(1998)Littlewood-Paley theory and function spaces with Math. Nachr. 189 221-242
[18]  
Piotrowska I(1998) weights Math. Nachr. 196 231-250
[19]  
Haroske D D(2012)Function spaces with exponential weights, I J. Funct. Anal. 262 1603-1629
[20]  
Skrzypczak L(2011)Function spaces with exponential weights, II Dissertationes Math. 478 1-78
12345