Composition Operators on Weighted Sobolev Spaces and the Theory of Q_p-Homeomorphisms

Composition Operators on Weighted Sobolev Spaces and the Theory of Q_p-Homeomorphisms Full article

Journal

Doklady Mathematics
ISSN: 1064-5624 , E-ISSN: 1531-8362

Output data

Year: 2020, Volume: 102, Number: 2, Pages: 371-375 Pages count : 5 DOI: 10.1134/S1064562420050440

Tags

Sobolev space, composition operator, quasiconformal analysis, capacity estimate

Authors

Vodopyanov S.K. ¹

Affiliations

1	Sobolev Institute of Mathematics

We define the scale Q_p , n-1<p<\infty, of homeomorphisms of spatial domains in 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 Q_n of mappings contains the class of so-called Q-homeomorphisms, which have been actively studied over the past 25 years. An equivalent functional and analytic description of these classes 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 Q_p .

Vodopyanov S.K.
Composition Operators on Weighted Sobolev Spaces and the Theory of Q_p-Homeomorphisms
Doklady Mathematics. 2020. V.102. N2. P.371-375. DOI: 10.1134/S1064562420050440 WOS Scopus OpenAlex

Водопьянов С.К.
ОПЕРАТОРЫ КОМПОЗИЦИИ ВЕСОВЫХ ПРОСТРАНСТВА СОБОЛЕВА И ТЕОРИЯ Q_p-ГОМЕОМОРФИЗМОВ
Доклады Академии наук. Серия: Математика, информатика, процессы управления. 2020. Т.494. №5. С.21--25. DOI: 10.31857/S268695432005046X OpenAlex

Submitted:	May 18, 2020
Accepted:	Jul 1, 2020

Web of science:	WOS:000607872900005
Scopus:	2-s2.0-85099409496
OpenAlex:	W3121101236

DB	Citing
Scopus	6
OpenAlex	10
Web of science	6