Multipliers of type (<i>p, q</i>)

Abstract

This paper is mainly concerned with generalisations of Hrmander's results on multipliers from L v (R n ) to L q (R n ) (see Hrmander [6]). Our principal results are that Hrmander'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 ^ oo and G is any LCA group. Here we use the author's work on quasimeasures in ' 'Quasimeasures and operators commuting with convolution" [4],