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Multipliers for vector valued functions
Published online by Cambridge University Press: 14 November 2011
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