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

Edmond Granirer

Colloquium Mathematicae (1994)

  • Volume: 67, Issue: 1, page 33-60
  • ISSN: 0010-1354

Abstract

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Let C V 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 C V p ( F ) , C V p ( F ) / M p ( F ) and C V 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 C V p ( F ) are considered. These improve results of Cowling and Fournier, Price and Edwards, Lust-Piquard, and others.

How to cite

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Granirer, Edmond. "On convolution operators with small support which are far from being convolution by a bounded measure." Colloquium Mathematicae 67.1 (1994): 33-60. <http://eudml.org/doc/210262>.

@article{Granirer1994,
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.},
author = {Granirer, Edmond},
journal = {Colloquium Mathematicae},
keywords = {convolution operators; locally compact groups; bounded measure},
language = {eng},
number = {1},
pages = {33-60},
title = {On convolution operators with small support which are far from being convolution by a bounded measure},
url = {http://eudml.org/doc/210262},
volume = {67},
year = {1994},
}

TY - JOUR
AU - Granirer, Edmond
TI - On convolution operators with small support which are far from being convolution by a bounded measure
JO - Colloquium Mathematicae
PY - 1994
VL - 67
IS - 1
SP - 33
EP - 60
AB - 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.
LA - eng
KW - convolution operators; locally compact groups; bounded measure
UR - http://eudml.org/doc/210262
ER -

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