Abstract
For an open subset \Omega of the Euclidean space \mathbf {R}^n, a measurable non-singular transformation T:\Omega \to \Omega and a real-valued measurable function u on \mathbf {R}^n, we study the weighted composition operator uC_T : f \mapsto u \cdot (f \circ T) on the Orlicz–Sobolev space W^{1, \varphi }(\Omega ) consisting of those functions of the Orlicz space L^{\varphi }(\Omega ) whose distributional derivatives of the first order belong to L^{\varphi }(\Omega ). We also discuss a sufficient condition under which uC_T is compact.
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| 2000 Mathematics Subject Classification:
primary 47B33, 47B38; secondary 46E30, 46E35
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| †indicates author for correspondence |
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