Characterization of Herz-type Besov-Morrey and Triebel-Lizorkin-Morrey Spaces

Ruslan Abdulkadirov; Pavel Lyakhov

doi:10.20944/preprints202304.0722.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 20 April 2023 / Approved: 21 April 2023 / Online: 21 April 2023 (10:43:57 CEST)

The main goal of this article is the characterization of Herz-type Besov-Morrey spaces K˙p,qαN˙μ,rs and Triebel-Lizorkin-Morrey spaces K˙p,qαE˙μ,rs via ball means of differences, atomic, molecular and wavelet decompositions. There are provided necessary facts for implying these results, which can help to explore such spaces on different domains in further researches. Proposed spaces allow to extend the class of studying functions, containing Leray projection, heat semi-group and other operators, which can be helpful in exploring weak, strong and mild solutions of nonlinear partial differential equations.

Herz-type Besov-Morrey spaces; Herz-type Triebel-Lizorkin-Morrey spaces; ball mean of differences; atomic and molecular decomposition; wavelet decomposition

Computer Science and Mathematics, Analysis

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Characterization of Herz-type Besov-Morrey and Triebel-Lizorkin-Morrey Spaces

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