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

Abstract

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

22 pages