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Multipliers from spaces of test functions to amalgams

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

Maria Torres De Squire
Maria Torres De Squire
Affiliation:
Department of Mathematics and StatisticsUniversity of ReginaRegina SaskatchewanCanadaS4S 0A2
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Abstract

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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.

MSC classification

Secondary: 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 1 , February 1993 , pp. 97 - 110
Copyright
Copyright © Australian Mathematical Society 1993

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