Functional and Analytical Properties of a Class of Mappings of Quasiconformal Analysis on Carnot Groups Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2022, Volume: 63, Number: 2, Pages: 233-261 Pages count : 29 DOI: 10.1134/S0037446622020045 | ||
| Tags | 517.518:517.54; capacity of a condenser; Carnot group; composition operator; quasiconformal analysis; Sobolev space | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | 0314-2019-0006 |
Abstract:
This article addresses the conceptual questions ofquasiconformal analysis on Carnot groups.We prove the equivalence of the three classes of homeomorphisms:the mappings of the first classinduce bounded composition operatorsfrom a weighted Sobolev space into an unweighted one;the mappings of the second classare characterized by way of estimatingthe capacity of the preimage of a condenserin terms of the weighted capacity of the condenser in the image;the mappings of the third classare described viaa pointwise relation between the norm of the matrix of the differential,the Jacobian,and the weight function.We obtain a new proof of the absolute continuity of mappings. © 2022, Pleiades Publishing, Ltd.
Cite:
Vodopyanov S.K.
, Evseev N.A.
Functional and Analytical Properties of a Class of Mappings of Quasiconformal Analysis on Carnot Groups
Siberian Mathematical Journal. 2022. V.63. N2. P.233-261. DOI: 10.1134/S0037446622020045 WOS Scopus РИНЦ OpenAlex
Functional and Analytical Properties of a Class of Mappings of Quasiconformal Analysis on Carnot Groups
Siberian Mathematical Journal. 2022. V.63. N2. P.233-261. DOI: 10.1134/S0037446622020045 WOS Scopus РИНЦ OpenAlex
Original:
Водопьянов С.К.
, Евсеев Н.А.
Функциональные и аналитические свойства одного класса отображений квазиконформного анализа на группах Карно
Сибирский математический журнал. 2022. Т.63. №2. С.283–315. DOI: 10.33048/smzh.2022.63.204 РИНЦ
Функциональные и аналитические свойства одного класса отображений квазиконформного анализа на группах Карно
Сибирский математический журнал. 2022. Т.63. №2. С.283–315. DOI: 10.33048/smzh.2022.63.204 РИНЦ
Identifiers:
| Web of science: | WOS:000778950000004 |
| Scopus: | 2-s2.0-85127927235 |
| Elibrary: | 48427746 |
| OpenAlex: | W4225972025 |