Functiones et Approximatio Commentarii Mathematici

Some properties of variable Besov-type spaces

Douadi Drihem

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Abstract

In this article we introduce Besov-type spaces with variable smoothness and integrability, which unify and generalize the Besov-type spaces with fixed exponents. Under natural regularity assumptions on the exponent functions, we show that our spaces are well-defined, i.e., independent of the choice of basis functions and we establish some properties of these function spaces. Moreover the Sobolev embeddings for these function spaces are obtained.

Article information

Source
Funct. Approx. Comment. Math., Volume 52, Number 2 (2015), 193-221.

Dates
First available in Project Euclid: 18 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.facm/1434650877

Digital Object Identifier
doi:10.7169/facm/2015.52.2.2

Mathematical Reviews number (MathSciNet)
MR3358316

Zentralblatt MATH identifier
1330.46031

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

Keywords
Besov spaces embeddings maximal function variable exponent

Citation

Drihem, Douadi. Some properties of variable Besov-type spaces. Funct. Approx. Comment. Math. 52 (2015), no. 2, 193--221. doi:10.7169/facm/2015.52.2.2. https://projecteuclid.org/euclid.facm/1434650877


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