Ball Average Characterizations of Variable Besov-type Spaces

Abstract

In this article, the authors characterize the variable Besov-type spaces $B_{p(\cdot),q(\cdot)}^{s(\cdot),\phi}(\mathbb{R}^n)$, with $1/p(\cdot)$ and $1/q(\cdot)$ satisfying the globally log-Hölder continuous conditions, via Peetre maximal functions and averages on balls. The latter characterization, via averages on balls, gives one way to introduce these spaces on metric measure spaces.