W1X上的复合算子必须由拟共形映射导出

Central European Journal of Mathematics Pub Date : 2014-04-01 DOI:10.2478/s11533-013-0392-8

L. Kleprlík

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引用次数: 2

摘要

设Ω∧∈n为开集，X(Ω)为靠近Lq(Ω)的任意重排不变函数空间，即X具有q标度性。证明了从W1X到W1X的复合算子u∈uℴf的每一个同胚f必然是一个q-拟共形映射。对于复合算子的充分性，给出了一些新的结果。

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Composition operators on W1X are necessarily induced by quasiconformal mappings

Let Ω ⊂ ℝn be an open set and X(Ω) be any rearrangement invariant function space close to Lq(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 W1X to W1X is necessarily a q-quasiconformal mapping. We also give some new results for the sufficiency of this condition for the composition operator.

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来源期刊

Central European Journal of Mathematics 数学-数学

自引率

0.00%

发文量

审稿时长

3-8 weeks