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 -moduli inequalities (-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.
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