A Mean Characterization of Weighted Anisotropic Besov and Triebel-Lizorkin Spaces

被引：11
|
作者：
Li, Baode [1 ]
Bownik, Marcin [2 ]
Yang, Dachun [3 ]
Yuan, Wen [3 ]
机构：
[1] Xinjiang Univ, Sch Math & Stat, Urumqi 830046, Peoples R China
[2] Univ Oregon, Dept Math, Eugene, OR 97403 USA
[3] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China
来源：
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 2014年 / 33卷 / 02期
基金：
高等学校博士学科点专项科研基金; 美国国家科学基金会; 中国国家自然科学基金;
关键词：
Anisotropic expansive dilation; Besov space; Triebel-Lizorkin space; Muckenhoupt weight; square function; MOLECULAR DECOMPOSITIONS; SINGULAR INTEGRALS; HARDY-SPACES; BOUNDEDNESS;
D O I：
10.4171/ZAA/1503
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, the authors study weighted anisotropic Besov and Triebel-Lizorkin spaces associated with expansive dilations and A(infinity)-weights. The authors show that elements of these spaces are locally integrable when the smoothness parameter alpha is positive. The authors also characterize these spaces for small values of alpha in terms of a mean square function recently introduced in the context of Sobolev spaces in [Math. Ann. 354 (2012), 589-626] and isotropic Triebel-Lizorkin spaces in [Publ. Mat. 57 (2013), 57-82].
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页码：125 / 147
页数：23
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