Composition operators on Sobolev spaces with a metric measure space as a domain. II

TL;DR

This paper characterizes the homeomorphisms that generate bounded composition operators on Sobolev spaces within metric measure space domains, extending understanding of function composition in these generalized settings.

Contribution

It provides a detailed description of the homeomorphisms inducing bounded composition operators on Sobolev spaces in metric measure spaces, advancing the theoretical framework.

Findings

Characterization of homeomorphisms inducing bounded composition operators

Extension of Sobolev space theory to metric measure spaces

New criteria for boundedness of composition operators

Abstract

We obtain a description of the homeomorphisms which induce bounded composition operators on Sobolev spaces of functions on metric measure spaces.