Geodesic
Composition operators on weighted Sobolev spaces and the theory of $\mathscr{Q}_p$-homeomorphisms
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 494 (2020), pp. 21-25 Cet article a éte moissonné depuis la source Math-Net.Ru

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We define the scale $\mathscr{Q}_p$, $n-1$, of homeomorphisms of spatial domains in $\mathbb{R}^n$, a geometric description of which is due to the control of the behavior of the p-capacity of condensers in the image through the weighted p-capacity of the condensers in the preimage. For $p=n$ the class $\mathscr{Q}_n$ of mappings contains the class of so-called $\mathscr{Q}_p$-homeomorphisms, which have been actively studied over the past 25 years. An equivalent functional and analytic description of these classes $\mathscr{Q}_p$ is obtained. It is based on the problem of the properties of the composition operator of a weighted Sobolev space into a nonweighted one induced by a map inverse to some of the class $\mathscr{Q}_p$.
Keywords: Sobolev space, composition operator, capacity estimate.
Mots-clés : quasiconformal analysis 
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     author = {S. K. Vodopyanov},
     title = {Composition operators on weighted {Sobolev} spaces and the theory of $\mathscr{Q}_p$-homeomorphisms},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {21--25},
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     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_494_a4/}
}
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S. K. Vodopyanov. Composition operators on weighted Sobolev spaces and the theory of $\mathscr{Q}_p$-homeomorphisms. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 494 (2020), pp. 21-25. http://geodesic.mathdoc.fr/item/DANMA_2020_494_a4/

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