TWO‑WEIGHTED COMPOSITION OPERATORS ON SOBOLEV SPACES AND QUASICONFORMAL ANALYSIS Full article
| Journal |
Journal of Mathematical Sciences (United States)
ISSN: 1072-3374 , E-ISSN: 1573-8795 |
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| Output data | Year: 2022, Pages: 1-19 Pages count : 19 DOI: 10.1007/s10958-022-05903-y | ||
| Tags | Weighted Sobolev space · Quasiconformal analysis · Composition operator · Capacity estimate | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0006 |
Abstract:
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.
Cite:
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
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
Dates:
| Accepted: | Sep 23, 2022 |
| Published online: | Sep 28, 2022 |
Identifiers:
| Scopus: | 2-s2.0-85139132549 |
| Elibrary: | 59747669 |
| OpenAlex: | W4297548875 |
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