Composition operators on Sobolev spaces and weighted moduli inequalities

Abstract

In this paper we study connections between composition operators on Sobolev spaces and mappings defined by $p$-moduli inequalities ($p$-capacity inequalities). We prove that weighted moduli inequalities lead to composition operators on corresponding Sobolev spaces and inverse, composition operators on Sobolev spaces imply weighted moduli inequalities.

11 pages. arXiv admin note: text overlap with arXiv:2110.09261