Continuous characterization of the Besov spaces of variable smoothness and integrability

  • S. Benmahmoud M'sila Univ., Laboratory Funct. Analysis and Geometry Spaces, Algeria
  • D. Drihem M'sila Univ., Laboratory Funct. Analysis and Geometry Spaces, Algeria
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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Published
17.01.2023
How to Cite
BenmahmoudS., and DrihemD. “Continuous Characterization of the Besov Spaces of Variable Smoothness and Integrability”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 12, Jan. 2023, pp. 1601 -24, doi:10.37863/umzh.v74i12.6578.
Section
Research articles