On mappings generating embedding operators in Sobolev classes on metric measure spaces

In this article, we study homeomorphisms $\phi :\mathrm{\Omega }\to \tilde{\mathrm{\Omega }}$ that generate embedding operators in Sobolev classes on metric measure spaces $X$ by the composition rule ${\phi }^{\ast }(f)=f\circ \phi$. In turn, this leads to Sobolev type embedding theorems for a wide class of bounded domains $\tilde{\mathrm{\Omega }}\subset X$.