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Title

On convolution operators with small support which are far from being convolution by a bounded measure

Authors 1

Affiliations

  1. Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2

Abstract

Let CVp(F) be the left convolution operators on Lp(G) with support included in F and Mp(F) denote those which are norm limits of convolution by bounded measures in M(F). Conditions on F are given which insure that CVp(F), CVpFMp(F) and CVpFW are as big as they can be, namely have l∞ as a quotient, where the ergodic space W contains, and at times is very big relative to Mp(F). Other subspaces of CVp(F) are considered. These improve results of Cowling and Fournier, Price and Edwards, Lust-Piquard, and others.

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Colloquium Mathematicum
1994/67/1
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Pages:
33-60
Main language of publication
English
Received
1993-05-17
Accepted
1993-08-25
Published
1994
Exact and natural sciences