Characterizations of Morrey type Besov and Triebel–Lizorkin spaces with variable exponents

In this paper, Morrey type Besov and Triebel–Lizorkin spaces with variable exponents are introduced. Then equivalent quasi-norms of these new spaces in terms of Peetreʼs maximal functions are obtained. Finally, applying those equivalent quasi-norms, the authors obtain the atomic, molecular and wavel...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2011-09, Vol.381 (1), p.280-298
Main Authors: Fu, Jingjing, Xu, Jingshi
Format: Article
Language:English
Subjects:
Atom
Besov space
Equivalent norm
Exact sciences and technology
Fourier analysis
Functional analysis
Mathematical analysis
Mathematics
Maximal function
Molecule
Morrey space
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Triebel–Lizorkin space
Variable exponent
Wavelet
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Summary:In this paper, Morrey type Besov and Triebel–Lizorkin spaces with variable exponents are introduced. Then equivalent quasi-norms of these new spaces in terms of Peetreʼs maximal functions are obtained. Finally, applying those equivalent quasi-norms, the authors obtain the atomic, molecular and wavelet decompositions of these new spaces.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2011.02.026