Coincidence of set functions in quasiconformal analysis Full article
| Journal |
Sbornik Mathematics
ISSN: 1064-5616 , E-ISSN: 1468-4802 |
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| Output data | Year: 2022, Volume: 213, Number: 9, Pages: 1157–1186 Pages count : 29 DOI: 10.4213/sm9702e | ||
| Tags | quasiconformal analysis, Sobolev space, composition operator, condenser capacity, outer operator distortion function, set function | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0006 |
Abstract:
It is known that mappings occurring in quasiconformal analysis can be defined in several equivalent ways: 1) as homeomorphisms inducing bounded composition operators between Sobolev spaces; 2) as Sobolev-class homeomorphisms with bounded distortion whose operator distortion function is integrable; 3) as homeomorphism changing the capacity of the image
of a condenser in a controllable way in terms of the weighted capacity of the condenser in the source space; 4) as homeomorphism changing the modulus of the image of a family of curves in a controllable way in terms of the weighted modulus of the family of curves in the source space. A certain set function, defined on open subsets, can be associated with each of these definitions.
The main result consists in the fact that all these set functions coincide.
Cite:
Vodopyanov S.K.
Coincidence of set functions in quasiconformal analysis
Sbornik Mathematics. 2022. V.213. N9. P.1157–1186. DOI: 10.4213/sm9702e WOS Scopus РИНЦ OpenAlex
Coincidence of set functions in quasiconformal analysis
Sbornik Mathematics. 2022. V.213. N9. P.1157–1186. DOI: 10.4213/sm9702e WOS Scopus РИНЦ OpenAlex
Original:
Водопьянов С.К.
О совпадении функций множества в квазиконформном анализе
Математический сборник. 2022. Т.213. №9. С.3-33. DOI: 10.4213/sm9702 РИНЦ OpenAlex
О совпадении функций множества в квазиконформном анализе
Математический сборник. 2022. Т.213. №9. С.3-33. DOI: 10.4213/sm9702 РИНЦ OpenAlex
Dates:
| Submitted: | Jan 27, 2022 |
| Accepted: | Feb 22, 2023 |
| Published online: | Mar 1, 2023 |
Identifiers:
| Web of science: | WOS:000992271700001 |
| Scopus: | 2-s2.0-85165898294 |
| Elibrary: | 59290788 |
| OpenAlex: | W4381306353 |