A characterization of Hajlasz-Sobolev and Triebel-Lizorkin spaces via grand Littlewood-Paley functions

被引：61

作者：

Koskela, Pekka ^{[1
]}

Yang, Dachun ^{[2
]}

Zhou, Yuan ^{[1
,2
]}

机构：

[1] Univ Jyvaskyla, Dept Math & Stat, FIN-40014 Jyvaskyla, Finland

[2] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2010年 / 258卷 / 08期

基金：

中国国家自然科学基金; 芬兰科学院;

关键词：

Sobolev spaces; Triebel-Lizorkin space; Calderon reproducing formula; HARDY-SPACES; DECOMPOSITIONS; TRANSFORM; METRICS;

D O I：

10.1016/j.jfa.2009.11.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we establish the equivalence between the Hajlasz-Sobolev spaces or classical Triebel-Lizorkin spaces and it class of grand Triebel-Lizorkin spaces on Euclidean spaces and also on metric spaces that are both doubling and reverse doubling. In particular, when p is an element of (n/(n + 1), infinity), we give a new characterization of the Hajlasz-Sobolev spaces (M) over dot(1),P (R-n) via a grand Littlewood-Paley function. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：2637 / 2661

页数：25

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