Abstract
SynopsisLet 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.
Publisher
Cambridge University Press (CUP)
Reference9 articles.
1. 9 Torrea J. L. . Andlisis de Fourier de Functiones vectoriales. Ph.D. Dissertation, Zaragoza, 1980.
2. Multipliers of group algebras of vector-valued functions
3. Linear functionals on the space of continuous mapping of a compact Hausdorff space into a Banach space;Singer;Rev. Math. Pures Appl.,1957
4. Characterisations of the right multipliers for L1(G,A)