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Weighted composition operators on Orlicz-Sobolev spaces

Part of: Linear function spaces and their duals Special classes of linear operators

Published online by Cambridge University Press:  09 April 2009

Subhash C. Arora ,
Gopal Datt  and
Satish Verma
Subhash C. Arora
Affiliation:
Department of MathematicsUniversity of DelhiDelhi-110007Indiae-mail: scarora@maths.du.ac.in
Gopal Datt
Affiliation:
Department of MathematicsPGDAV CollegeUniversity of DelhiDelhi-110065Indiae-mail: gopaldatt@maths.du.ac.in
Satish Verma
Affiliation:
Department of MathematicsSGTB Khalsa CollegeUniversity of DelhiDelhi-110007Indiae-mail: vermas@maths.du.ac.in
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Abstract

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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

Secondary: 47B33: Composition operators 47B38: Operators on function spaces (general) 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46E35: Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

Information

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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