Generalised Hajłasz-Besov spaces on $RD$-spaces

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