Taiwanese Journal of Mathematics

Ball Average Characterizations of Variable Besov-type Spaces

Ciqiang Zhuo, Der-Chen Chang, and Dachun Yang

Full-text: Open access

Abstract

In this article, the authors characterize the variable Besov-type spaces $B_{p(\cdot),q(\cdot)}^{s(\cdot),\phi}(\mathbb{R}^n)$, with $1/p(\cdot)$ and $1/q(\cdot)$ satisfying the globally log-Hölder continuous conditions, via Peetre maximal functions and averages on balls. The latter characterization, via averages on balls, gives one way to introduce these spaces on metric measure spaces.

Article information

Source
Taiwanese J. Math., Volume 23, Number 2 (2019), 427-452.

Dates
Received: 7 May 2018
Accepted: 3 December 2018
First available in Project Euclid: 21 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1545361215

Digital Object Identifier
doi:10.11650/tjm/181204

Mathematical Reviews number (MathSciNet)
MR3936007

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Secondary: 42B35: Function spaces arising in harmonic analysis

Keywords
Besov space variable exponent ball average Peetre maximal function

Citation

Zhuo, Ciqiang; Chang, Der-Chen; Yang, Dachun. Ball Average Characterizations of Variable Besov-type Spaces. Taiwanese J. Math. 23 (2019), no. 2, 427--452. doi:10.11650/tjm/181204. https://projecteuclid.org/euclid.twjm/1545361215


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