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

100%

Kleprlík L.

Open Mathematics

2014

tom 12

nr 8

1229-1238

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.

Composition operator and Sobolev-Lorentz spaces $WL^{n,q}$

51%

Hencl S., Kleprlík L., Malý J.

Studia Mathematica

2014

tom 221

nr 3

197-208

Let Ω,Ω' ⊂ ℝⁿ be domains and let f: Ω → Ω' be a homeomorphism. We show that if the composition operator $T_{f}: u ↦ u∘ f$ maps the Sobolev-Lorentz space $WL^{n,q}(Ω')$ to $WL^{n,q}(Ω)$ for some q ≠ n then f must be a locally bilipschitz mapping.

Ograniczanie wyników

1 Open Mathematics

1 Studia Mathematica

2 Kleprlík L.

1 Hencl S.

1 Malý J.

2 2014

Wyniki wyszukiwania

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

Composition operator and Sobolev-Lorentz spaces $WL^{n,q}$