Wavelet decomposition and embeddings of generalised Besov-Morrey spaces

We study embeddings between generalised Besov-Morrey spaces Ns phi,p,q(Rd). Both sufficient and necessary conditions for the embeddings are proved. Embeddings of the Besov-Morrey spaces into the Lebesgue spaces Lr(Rd) are also considered. Our approach requires a wavelet characterisation of the spaces which we establish for the system of Daubechies wavelets. (c) 2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

This study investigates embeddings between generalised Besov-Morrey spaces Ns phi,p,q(Rd), proving both sufficient and necessary conditions for the embeddings. The embeddings of Besov-Morrey spaces into Lebesgue spaces Lr(Rd) are also discussed. The approach used in this study involves wavelet characterisation of spaces established for the Daubechies wavelets system.