Banach Journal of Mathematical Analysis

Herz--Morrey type Besov and Triebel-Lizorkin spaces with variable exponents

Baohua Dong and Jingshi Xu

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Abstract

In the article, the boundedness of vector-valued sublinear operators in Herz--Morrey spaces with variable exponents $M\dot{K}^{\alpha(\cdot),\lambda}_{q,p(\cdot)}(\mathbb{R}^{n})$ are obtained. Then Herz--Morrey type Besov and Triebel-Lizorkin spaces with variable exponents are introduced. Finally, we prove the equivalent quasi-norms on these spaces by Peetre's maximal operators.

Article information

Source
Banach J. Math. Anal. Volume 9, Number 1 (2015), 75-101.

Dates
First available in Project Euclid: 19 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1419000579

Digital Object Identifier
doi:10.15352/bjma/09-1-7

Mathematical Reviews number (MathSciNet)
MR3296087

Zentralblatt MATH identifier
1333.46026

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Secondary: 42B25: Maximal functions, Littlewood-Paley theory 42B35: Function spaces arising in harmonic analysis

Keywords
Variable exponent Herz--Morrry space Besov space Triebel--Lizorkin space maximal operator

Citation

Dong, Baohua; Xu, Jingshi. Herz--Morrey type Besov and Triebel-Lizorkin spaces with variable exponents. Banach J. Math. Anal. 9 (2015), no. 1, 75--101. doi:10.15352/bjma/09-1-7. https://projecteuclid.org/euclid.bjma/1419000579


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