Continuous characterization of the Besov spaces of variable smoothness and integrability

S.  Benmahmoud; D.  Drihem

doi:10.37863/umzh.v74i12.6578

S. Benmahmoud M'sila Univ., Laboratory Funct. Analysis and Geometry Spaces, Algeria
D. Drihem M'sila Univ., Laboratory Funct. Analysis and Geometry Spaces, Algeria

DOI: https://doi.org/10.37863/umzh.v74i12.6578

Keywords: Besov space, variable exponent, Calderón reproducing formula.

Abstract

UDC 517.9

We obtain new equivalent quasinorms of the Besov spaces of variable smoothness and integrability. Our main tools are the continuous version of the Calderón reproducing formula, maximal inequalities, and the variable-exponent technique; however, allowing the parameters to vary from point to point leads to additional difficulties which, in general, can be overcome by imposing regularity assumptions on these exponents.

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