Abstract:
We prove that the two approaches to describing homeomorphisms in modern quasiconformal analysis are equivalent: A homeomorphism changes under control the capacity of the image of a condenser in terms of the weighted capacity of a condenser in the preimage if and only if the modulus of the image of a family of curves can be estimated in terms of the weighted modulus of the original family of curves.
Keywords:
quasiconformal analysis, Sobolev space, composition operator, capacity estimate, modulus of a family of curves.
The author was supported by the Mathematical Center in Akademgorodok and the Ministry of Science and
Higher Education of the Russian Federation (Contract 075–15–2019–1613).
Citation:
S. K. Vodopyanov, “On the equivalence of two approaches to problems of quasiconformal analysis”, Sibirsk. Mat. Zh., 62:6 (2021), 1252–1270; Siberian Math. J., 62:6 (2021), 1010–1025
\Bibitem{Vod21}
\by S.~K.~Vodopyanov
\paper On the equivalence of two approaches to problems of quasiconformal analysis
\jour Sibirsk. Mat. Zh.
\yr 2021
\vol 62
\issue 6
\pages 1252--1270
\mathnet{http://mi.mathnet.ru/smj7626}
\crossref{https://doi.org/10.33048/smzh.2021.62.604}
\elib{https://elibrary.ru/item.asp?id=47533693}
\transl
\jour Siberian Math. J.
\yr 2021
\vol 62
\issue 6
\pages 1010--1025
\crossref{https://doi.org/10.1134/S0037446621060045}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000723707400004}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85120164635}
Linking options:
https://www.mathnet.ru/eng/smj7626
https://www.mathnet.ru/eng/smj/v62/i6/p1252
This publication is cited in the following 6 articles:
S. K. Vodopyanov, S. V. Pavlov, “O granichnykh znacheniyakh v geometricheskoi teorii funktsii v oblastyakh s podvizhnymi granitsami”, Sib. matem. zhurn., 65:3 (2024), 489–516
VLADIMIR GOL'DSHTEIN, EVGENY SEVOST'YANOV, ALEXANDER UKHLOV, “COMPOSITION OPERATORS ON SOBOLEV SPACES AND”, MR, 26(76):2 (2024), 101
S. K. Vodopyanov, S. V. Pavlov, “Boundary Values in the Geometric Function Theory in Domains with Moving Boundaries”, Sib Math J, 65:3 (2024), 552
A. O. Tomilov, “An estimate for the measure of the preimage of a ball under $Q_{q,p}$-homeomorphisms”, Siberian Math. J., 65:6 (2024), 1395–1401
Izv. Math., 87:4 (2023), 683–725
S. K. Vodopyanov, “Coincidence of set functions in quasiconformal analysis”, Sb. Math., 213:9 (2022), 1157–1186
Citation in format AMSBIB
Contact us: