Regularity of the inverse of a homeomorphism of a Sobolev–Orlicz space


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Given a homeomorphism ϕ ∈ WM1, we determine the conditions that guarantee the belonging of the inverse of ϕ in some Sobolev–Orlicz space WF1. We also obtain necessary and sufficient conditions under which a homeomorphism of domains in a Euclidean space induces the bounded composition operator of Sobolev–Orlicz spaces defined by a special class of N-functions. Using these results, we establish requirements on a mapping under which the inverse homeomorphism also induces the bounded composition operator of another pair of Sobolev–Orlicz spaces which is defined by the first pair.

作者简介

A. Menovshchikov

Sobolev Institute of Mathematics Novosibirsk State University; Peoples’ Friendship University of Russia

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