Bad behavior and inclusion results for multipliers of type (<i>p, q</i>)

Abstract

This paper is concerned with the space of multipliers from L p (G) to L Q (G) for various pairs of indices p and q, where G is an LCA group. We show that if l^p<2<q^co 9 and G is noncompact, then there are multipliers of type (p, q) whose 'Fourier transforms' are not measures. This is an extension of a result of Hrmander, and completes work begun in two earlier papers (this journal, 1966). In the second part, we show that if G is infinite, many of the natural inclusion relations between spaces of multipliers are proper.