The Haar system in Besov-type spaces

被引：6
|
作者：
Yuan, Wen [1 ]
Sickel, Winfried [2 ]
Yang, Dachun [1 ]
机构：
[1] Beijing Normal Univ, Sch Math Sci, Minist Educ China, Lab Math & Complex Syst, Beijing 100875, Peoples R China
[2] Friedrich Schiller Univ Jena, Math Inst, D-07743 Jena, Germany
来源：
STUDIA MATHEMATICA | 2020年 / 253卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Besov space; Besov-type space; characteristic function; orthonormal Haar system; smooth wavelets; MORREY SPACES; MAXIMAL FUNCTIONS; INTERPOLATION; EQUATIONS; BASES; MULTIPLIERS;
D O I：
10.4064/sm180828-9-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Some Besov-type spaces B-p,q(s,tau)(R-n) can be characterized in terms of the behavior of the Fourier-Haar coefficients. In this article, the authors discuss some necessary restrictions on the parameters s, tau, p, q and n in order to have such a characterization. To do so, the authors measure the regularity of the characteristic function X of the unit cube in R-n via Besov-type spaces B-p,q(s,tau)(R-n). Furthermore, the authors study necessary and sufficient conditions for the operation < f,X > to generate a continuous linear functional on B-p,q(s,tau)(R-n).
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页码：129 / 162
页数：34
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