Hardy Inequalities in Triebel-Lizorkin Spaces

被引：5
作者：
Ihnatsyeva, Lizaveta [1 ]
Vahakangas, Antti V. [1 ]
机构：
[1] Univ Helsinki, Dept Math & Stat, FI-00014 Helsinki, Finland
来源：
INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2013年 / 62卷 / 06期
基金：
芬兰科学院;
关键词：
Triebel-Lizorkin space; Ahlfors d-regular set; Hardy inequality; pointwise multiplier; extension theorem; local polynomial approximation; SMOOTH FUNCTIONS; TRACES; DOMAINS;
D O I：
10.1512/iumj.2013.62.5173
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove an inequality of Hardy type for functions in Triebel-Lizorkin spaces. The distance involved is measured to a given Ahlfors d-regular set in R-n, with n - 1 < d < n. As an application of the Hardy inequality, we consider boundedness of pointwise multiplication operators, and extension problems.
引用
收藏
页码：1785 / 1807
页数：23
相关论文
共 33 条
[1]  
Adams David R., 1996, GRUND MATH WISS, V314
[2]   On pointwise multipliers for FSp,q(Rn) in case σp,q&lt; S &lt; n/p(*) [J].
Sickel W. .
Annali di Matematica Pura ed Applicata, 1999, 176 (1) :209-250
[3]  
[Anonymous], 1971, Tr. Mosk. Mat. Obs.
[4]  
[Anonymous], 2003, Ann. Mat. Pura Appl.
[5]  
BESOV OLEG V., 1979, SCRIPTA SERIES MATH
[6]  
BESOV OLEG V., 1978, SCRIPTA SERIES MATH
[7]   Extending Sobolev functions with partially vanishing traces from locally (ε, δ)-domains and applications to mixed boundary problems [J].
Brewster, Kevin ;
Mitrea, Dorina ;
Mitrea, Irina ;
Mitrea, Marius .
JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 266 (07) :4314-4421
[8]  
Brudnyi A, 2007, CONTEMP MATH, V445, P19
[9]   Approximation by functions of compact support in Besov-Triebel-Lizorkin spaces on irregular domains [J].
Caetano, AM .
STUDIA MATHEMATICA, 2000, 142 (01) :47-63
[10]  
Calderon A.-P., 1961, P S PURE MATH, V4, P33
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