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arXiv · 2110.09261

Composition operators on Sobolev spaces, $Q$-mappings and weighted Sobolev inequalities

Alexander Menovschikov·Alexander Ukhlov
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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.

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Alexander Menovschikov, Alexander Ukhlov. 2021-10-18. Composition operators on Sobolev spaces, $Q$-mappings and weighted Sobolev inequalities. https://arxiv.org/abs/2110.09261

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