A. V. Menovshchikov, “The lower semicontinuity of distortion coefficients of the homeomorphisms inducing bounded composition operators of Sobolev–Orlicz spaces”, Sibirsk. Mat. Zh., 2018, Volume 59, Number 2,Pages <nobr>422

The lower semicontinuity of distortion coefficients of the homeomorphisms inducing bounded composition operators of Sobolev–Orlicz spaces

A. V. Menovshchikov^abc

^a Sobolev Institute of Mathematics, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia
^c Peoples' Friendship University of Russia, Moscow, Russia

Abstract: We determine the conditions under which the locally uniform limit of mappings generating bounded composition operators of Sobolev–Orlicz spaces also generates an operator of this kind. We estimate the distortion coefficient of the limit mapping.

Keywords: Sobolev–Orlicz space, distortion, codistortion, biting convergence, composition operator, $N$-function.

UDC: 517.518+517.54

Received: 28.06.2017

DOI: 10.17377/smzh.2018.59.216