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Published online by Cambridge University Press: 09 April 2009
In this paper we study the space of multipliers M(r, s: p, q) from the space of test functions Φrs(G), on a locally compact abelian group G, to amalgams (Lp, lq)(G); the former includes (when r = s = ∞) the space of continuous functions with compact support and the latter are extensions of the Lp(G) spaces. We prove that the space M(∞: p) is equal to the derived space (Lp)0 defined by Figá-Talamanca and give a characterization of the Fourier transform for amalgams in terms of these spaces of multipliers.