The Lower Semicontinuity of Distortion Coefficients of the Homeomorphisms Inducing Bounded Composition Operators of Sobolev–Orlicz Spaces


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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.

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A. Menovshchikov

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

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