English

Composition operators on Sobolev spaces and weighted moduli inequalities

Analysis of PDEs 2021-12-22 v1

Abstract

In this paper we study connections between composition operators on Sobolev spaces and mappings defined by pp-moduli inequalities (pp-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.

Keywords

Cite

@article{arxiv.2112.11418,
  title  = {Composition operators on Sobolev spaces and weighted moduli inequalities},
  author = {Vladimir Gol'dshtein and Evgeny Sevost'yanov and Alexander Ukhlov},
  journal= {arXiv preprint arXiv:2112.11418},
  year   = {2021}
}

Comments

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

R2 v1 2026-06-24T08:26:43.211Z