Besov-Morrey spaces and differences (extended version)

TL;DR

This paper characterizes Besov-Morrey spaces using higher-order differences and establishes necessary and sufficient conditions for these characterizations, advancing the understanding of their structure.

Contribution

It provides new characterizations of Besov-Morrey spaces via differences and identifies conditions that are both necessary and sufficient.

Findings

Characterization of Besov-Morrey spaces through higher-order differences

Identification of necessary and sufficient conditions for these characterizations

Enhanced understanding of the structure of Besov-Morrey spaces

Abstract

We study the Besov-Morrey spaces $ \mathcal{N}^{s}_{u,p,q}(\mathbb{R}^{d}) $ and show that under certain conditions on the parameters these spaces can be characterized in terms of higher-order differences. Furthermore we prove that some of the mentioned conditions are also necessary.