Composition operators on W 1 X are necessarily induced by quasiconformal mappings

• Autorzy: Luděk Kleprlík
• Języki publikacji: EN

Abstrakty

EN

Let Ω ⊂ ℝn be an open set and X(Ω) be any rearrangement invariant function space close to L q(Ω), i.e. X has the q-scaling property. We prove that each homeomorphism f which induces the composition operator u ↦ u ℴ f from W 1 X to W 1 X is necessarily a q-quasiconformal mapping. We also give some new results for the sufficiency of this condition for the composition operator.

Słowa kluczowe

EN

Sobolev space; Rearrangement invariant space; Quasiconformal mappings; Composition operator

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
• 30C65: Quasiconformal mappings in 𝐑 n , other generalizations
• 47B33: Composition operators

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 8
• Strony: 1229-1238

Daty

wydano

2014-08-01

online

2014-05-08

Twórcy

autor

Luděk Kleprlík

• Charles University

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Identyfikatory

DOI

10.2478/s11533-013-0392-8