A remark on Besov spaces interpolation over the 2-adic group

TL;DR

This paper explores the relationships and interpolation properties of Besov spaces over the 2-adic group, motivated by recent results linking a specific Besov space to functions of bounded variation.

Contribution

It provides new insights into the functional relationships and interpolation properties of Besov spaces on the 2-adic group, building on recent identifications with BV spaces.

Findings

Identifies relationships between Besov spaces over the 2-adic group.

Establishes interpolation results for these Besov spaces.

Connects Besov spaces with BV functions in the 2-adic setting.

Abstract

Motivated by a recent result which identifies in the special setting of the 2-adic group the Besov space $\dot{B}^{1,\infty}_{1}(\mathbb{Z}_2)$ with $BV(\mathbb{Z}_2)$, the space of function of bounded variation, we study in this article some functional relationships between Besov spaces.