Vol. 35, No. 1, 1970

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

Garth Ian Gaudry

Vol. 35 (1970), No. 1, 83–94

To my teachers, Bert Bundesen and Peter Lettice This paper is concerned with the space of multipliers from Lp(G) to Lq(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
Received: 24 October 1969
Published: 1 October 1970
Garth Ian Gaudry