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Weighted composition operators on Orlicz-Sobolev spaces
Published online by Cambridge University Press: 09 April 2009
Abstract
For an open subset Ω of the Euclidean space Rn, a measurable non-singular transformation T: Ω → Ω and a real-valued measurable function u on Rn, we study the weighted composition operator uCτ: f ↦ u · (f º T) on the Orlicz-Sobolev space W1·Ψ (Ω) consxsisting of those functions of the Orlicz space LΨ (Ω) whose distributional derivatives of the first order belong to LΨ (Ω). We also discuss a sufficient condition under which uCτ is compact.
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 83 , Issue 3 , December 2007 , pp. 327 - 334
- Copyright
- Copyright © Australian Mathematical Society 2007
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