Generalised Hajłasz-Besov spaces on $RD$-spaces

Abstract

An $RD$ space is a doubling measure metric space $\Omega$ with the additional property that it has a reverse doubling property. In this paper we introduce a new class of Hajłasz-Besov spaces on $\Omega$ and extend several results from classical theory, such as embeddings and Sobolev-type embeddings.