TY - JOUR

T1 - Regularity of the inverse of a homeomorphism of a Sobolev–Orlicz space

AU - Menovshchikov, A. V.

N1 - Publisher Copyright: © 2017, Pleiades Publishing, Ltd.

PY - 2017/7/1

Y1 - 2017/7/1

N2 - Given a homeomorphism ϕ ∈ WM 1, we determine the conditions that guarantee the belonging of the inverse of ϕ in some Sobolev–Orlicz space WF 1. 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.

AB - Given a homeomorphism ϕ ∈ WM 1, we determine the conditions that guarantee the belonging of the inverse of ϕ in some Sobolev–Orlicz space WF 1. 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.

KW - codistortion

KW - composition operator

KW - distortion

KW - N-function

KW - Sobolev–Orlicz space

KW - FINITE DISTORTION

KW - Sobolev-Orlicz space

KW - DERIVATIVES

KW - OPERATORS

KW - QUASICONFORMAL MAPPINGS

KW - EXTREMAL MAPPINGS

UR - http://www.scopus.com/inward/record.url?scp=85028527327&partnerID=8YFLogxK

U2 - 10.1134/S0037446617040115

DO - 10.1134/S0037446617040115

M3 - Article

AN - SCOPUS:85028527327

VL - 58

SP - 649

EP - 662

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 4

ER -