Bad behavior and inclusion results for multipliers of type (p, q)

Garth Ian Gaudry

Vol. 35 (1970), No. 1, 83–94

DOI: 10.2140/pjm.1970.35.83

Abstract

To my teachers, Bert Bundesen and Peter Lettice 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 1 ≦ p < 2 < q ≦∞, 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 Hörmander, 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.

Mathematical Subject Classification

Primary: 42.50

Milestones

Received: 24 October 1969

Published: 1 October 1970