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

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