Wavelet decomposition and embeddings of generalised Besov-Morrey spaces

TL;DR

This paper investigates the conditions under which generalized Besov-Morrey spaces embed into each other and into Lebesgue spaces, using wavelet characterizations to establish these embeddings.

Contribution

It provides necessary and sufficient conditions for embeddings between generalized Besov-Morrey spaces and introduces a wavelet-based approach for characterizing these spaces.

Findings

Established wavelet characterisation of generalized Besov-Morrey spaces.

Derived necessary and sufficient conditions for embeddings.

Analyzed embeddings into Lebesgue spaces.

Abstract

We study embeddings between generalised Besov-Morrey spaces. Both sufficient and necessary conditions for the embeddings are proved. Embeddings of the Besov-Morrey spaces into the Lebesgue spaces are also considered. Our approach requires a wavelet characterisation of the spaces which we establish for the system of Daubechies wavelets.