Variable exponent Besov-Morrey spaces

TL;DR

This paper introduces variable exponent Besov-Morrey spaces, exploring their fundamental properties, decompositions, and key inequalities, expanding the framework of non-standard function spaces with variable indices.

Contribution

It defines and analyzes variable exponent Besov-Morrey spaces, including their atomic/molecular decompositions and a convolution inequality, advancing the theory of variable exponent function spaces.

Findings

Established fundamental properties of variable exponent Besov-Morrey spaces

Developed atomic and molecular decompositions for these spaces

Proved a convolution inequality with radial kernels

Abstract

In this paper we introduce Besov-Morrey spaces with all indices variable and study some fundamental properties. This includes a description in terms of Peetre maximal functions and atomic and molecular decompositions. This new scale of non-standard function spaces requires the introduction of variable exponent mixed Morrey-sequence spaces, which in turn are defined within the framework of semimodular spaces. In particular, we obtain a convolution inequality involving special radial kernels, which proves to be a key tool in this work.