Sobolev homeomorphisms and composition operators on homogeneous Lie groups

Abstract

In this article, we study Sobolev homeomorphisms and composition operators on homogeneous Lie groups. We prove that a measurable homeomorphism $\ddot{I}†:\hat{I}\text{c◯}\to \tilde{\hat{I}}\text{c◯}$ belongs to the Sobolev space $L_q^1(\hat{I}\text{c◯};\tilde{\hat{I}}\text{c◯})$, $1\le q<\infty$, if and only if $\ddot{I}†$ generates a bounded composition operator on Sobolev spaces.

14 pages