Regularity of convolution operators

H.D. Fegan

Vol. 178 (1997), No. 1, 53–62

DOI: 10.2140/pjm.1997.178.53

Abstract

In this paper we prove that any operator which is given by convolution with a suitable distribution on a compact semisimple Lie group is of type (,). Our main result is:

Theorem 1.1: If K is an operator defined by convolution, so Kf = k ∗f, then, for suitable distributions k, the operator K has the type (,).

Milestones

Received: 31 October 1994

Revised: 22 February 1995

Published: 1 March 1997