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Composition operators on Sobolev spaces, $Q$-mappings and weighted Sobolev inequalities (2110.09261v2)
Published 18 Oct 2021 in math.AP
Abstract: In this paper we give connections between mappings which generate bounded composition operators on Sobolev spaces and $Q$-mappings. On this base we obtain measure distortion properties $Q$-homeomorphisms. Using the composition operators on Sobolev spaces we obtain weighted Sobolev inequalities with special weights which are Jacobians of $Q$-mappings.