Multipliers of type (p, q)

Garth Ian Gaudry

Vol. 18 (1966), No. 3, 477–488

DOI: 10.2140/pjm.1966.18.477

Abstract

This paper is mainly concerned with generalisations of Hörmander’s results on multipliers from L^p(Rⁿ) to L^q(Rⁿ) (see Hörmander [6]). Our principal results are that Hörmander’s Theorem 1.12 and Corollary 1.5 continue to hold for any LCA group with an infinite discrete subgroup. In order to establish and formulate our results, we define the Fourier transform of functions in L^p(G) where 1 ≦ p ≦∞ and G is any LCA group. Here we use the author’s work on quasimeasures in “Quasimeasures and operators commuting with convolution” [4].

Mathematical Subject Classification

Primary: 46.80

Secondary: 42.56

Milestones

Received: 18 June 1965

Published: 1 September 1966