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

Volume 67 / 1994

Edmond Granirer Colloquium Mathematicum 67 (1994), 33-60 DOI: 10.4064/cm-67-1-33-60

Abstract

Let $CV_p(F)$ be the left convolution operators on $L^p(G)$ with support included in F and $M_p(F)$ denote those which are norm limits of convolution by bounded measures in M(F). Conditions on F are given which insure that $CV_p(F)$, $CV_p(F)/M_p(F)$ and $CV_p(F)/W$ 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 $M_p(F)$. Other subspaces of $CV_p(F)$ are considered. These improve results of Cowling and Fournier, Price and Edwards, Lust-Piquard, and others.

Authors

  • Edmond Granirer

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