TWO‑WEIGHTED COMPOSITION OPERATORS ON SOBOLEV SPACES AND QUASICONFORMAL ANALYSIS | Sciact - Система учета научной деятельности ИМ СО РАН

TWO‑WEIGHTED COMPOSITION OPERATORS ON SOBOLEV SPACES AND QUASICONFORMAL ANALYSIS Научная публикация

Журнал

Journal of Mathematical Sciences (United States)
ISSN: 1072-3374 , E-ISSN: 1573-8795

Вых. Данные

Год: 2022, Страницы: 1-19 Страниц : 19 DOI: 10.1007/s10958-022-05903-y

Ключевые слова

Weighted Sobolev space · Quasiconformal analysis · Composition operator · Capacity estimate

Авторы

Vodopyanov S.K. ¹

Организации

1	Sobolev Institute of Mathematics, Acad. Koptyug av.4, 630090 Novosibirsk, Russia

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2022-0006

We establish some equivalent conditions for a homeomorphism φ:D→D^' of Euclidean domains in R^n, n≥2, to induce a bounded composition operator φ*:L_p^1 (D';ω)∩Lip_l⁡(D' )→L_q^1 (D;θ), where 1<q≤p<∞, by the composition rule: φ*(f)=f∘φ. Here ω:D'→(0,∞) is an arbitrary weight function on the domain D', and θ:D→(0,∞) is some weight function in Muckenhoupt's A_q-class on the domain D. Moreover, we prove that the class of homeomorphisms under consideration is completely determined by the controlled variation of the weighted capacity of cubical condensers whose shells are concentric cubes.

Vodopyanov S.K.
TWO‑WEIGHTED COMPOSITION OPERATORS ON SOBOLEV SPACES AND QUASICONFORMAL ANALYSIS
Journal of Mathematical Sciences (United States). 2022. P.1-19. DOI: 10.1007/s10958-022-05903-y Scopus РИНЦ OpenAlex

Принята к публикации:	23 сент. 2022 г.
Опубликована online:	28 сент. 2022 г.

Scopus:	2-s2.0-85139132549
РИНЦ:	59747669
OpenAlex:	W4297548875

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