On a new characterisation of Besov spaces with negative exponents

TL;DR

This paper presents an alternative proof for characterizing Besov spaces with negative exponents using the integrability of harmonic functions weighted by their distance to the boundary.

Contribution

It introduces a new approach to characterize Besov spaces with negative exponents through harmonic function integrability, offering a different perspective from existing methods.

Findings

Provides a new proof technique for Besov space characterization.

Establishes a link between harmonic function integrability and Besov spaces.

Enhances understanding of function space properties with negative smoothness.

Abstract

We give an alternative proof of the characterization of Besov spaces with negative exponents by means of integrability of harmonic functions with a weight depending on the distance to the boundary.