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Multipliers for vector valued functions

Published online by Cambridge University Press:  14 November 2011

José Luis Torrea
José Luis Torrea
Affiliation:
Division de Matematicas, Universidad Autonoma de Madrid, Canto Blanco, Madrid 34, Spain
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Extract

Let G be a locally compact abelian group and let Γ be the dual of G. Let A, B be Banach spaces and Lp(G,A) the Bochner-Lebesgue spaces. We prove that the space of bounded linear translation invariant operators from L1(G, A) to LX(G, B) can be identified with the space of bounded convolution invariant (in some sense) operators and also with the space of a(A, B)-valued “weak regular” measures with the relation Tf = f *μ. (A. The existence of a function m∈ L∞ (Γ,α(A,B)), such that is also proved.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 99 , Issue 1-2 , 1984 , pp. 137 - 143
Copyright
Copyright © Royal Society of Edinburgh 1984

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