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Weighted composition operators on Orlicz-Sobolev spaces

Published online by Cambridge University Press:  09 April 2009

Subhash C. Arora
Affiliation:
Department of MathematicsUniversity of DelhiDelhi-110007Indiae-mail: [email protected]
Gopal Datt
Affiliation:
Department of MathematicsPGDAV CollegeUniversity of DelhiDelhi-110065Indiae-mail: [email protected]
Satish Verma
Affiliation:
Department of MathematicsSGTB Khalsa CollegeUniversity of DelhiDelhi-110007Indiae-mail: [email protected]
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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: fu · (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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2007

References

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