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

Granirer, Edmond

Colloquium Mathematicae, Tome 67 (1994), p. 33-60 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $l^{\infty}$ 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.

Publié le : 1994-01-01

Zbl 0841.43008

EUDML-ID : urn:eudml:doc:210262

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     author = {Edmond Granirer},
     title = {On convolution operators with small support which are far from being convolution by a bounded measure},
     journal = {Colloquium Mathematicae},
     volume = {67},
     year = {1994},
     pages = {33-60},
     zbl = {0841.43008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv67i1p33bwm}
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Granirer, Edmond. On convolution operators with small support which are far from being convolution by a bounded measure. Colloquium Mathematicae, Tome 67 (1994) pp. 33-60. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv67i1p33bwm/

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