Variable 2-Microlocal Besov–Triebel–Lizorkin-Type Spaces

被引：0

作者：

Su Qing WU ^{[1
]}

Da Chun YANG ^{[1
]}

Wen YUAN ^{[1
]}

Ci Qiang ZHUO ^{[2
]}

机构：

[1] Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University

[2] Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), College of Mathematics and Computer Science, Hu’nan Normal University

来源：

Acta Mathematica Sinica,English Series | 2018年 / 34卷 / 04期

基金：

中国国家自然科学基金;

关键词：

2-Microlocal Besov space; 2-Microlocal Triebel–Lizorkin space; variable exponent; φ-transform; Peetre maximal function; difference; atom; embedding;

D O I：

暂无

中图分类号：

O174 [函数论];

学科分类号：

070104 ;

摘要：

This article is devoted to the study of variable 2-microlocal Besov-type and Triebel–Lizorkin-type spaces. These variable function spaces are defined via a Fourier-analytical approach. The authors then characterize these spaces by means of φ-transforms, Peetre maximal functions, smooth atoms, ball means of differences and approximations by analytic functions. As applications, some related Sobolev-type embeddings and trace theorems of these spaces are also established. Moreover, some obtained results, such as characterizations via approximations by analytic functions, are new even for the classical variable Besov and Triebel–Lizorkin spaces.

引用

页码：699 / 748

页数：50

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