J Austral Math Soc Ser A 54 pp97--110, 1993.

Multipliers from Spaces of Test Functions to Amalgams

Maria Torres de Squire

Abstract

In this paper we study the space of multipliers M(r, s : p, q) from the space of test functions F_rs(G) on a locally compact abelian group G, to amalgams (L^p, l^q)(G) ; the former includes (when r = s = ¥) the space of continuous functions with compact support and the latter are extensions of the L^p(G) spaces. We prove that the space M(¥: p) is equal to the derived space (L^p)₀ defined by Figá-Talamanca and give a characterization of the Fourier transform for amalgams in terms of these spaces of multipliers.

1991 AMS Subject Classification: 43A22

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Authors

Maria Torres de Squire

Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, Canada S4S 0A2.