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Convolution of Lp Functions on Non-Unimodular Groups

Published online by Cambridge University Press:  20 November 2018

Paul Milnes
Paul Milnes*
Affiliation:
University of Toronto, Toronto, Ontario
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In this note we prove the following

Theorem. If G is a nonunimodular locally compact group and 1<p<∞, then there is an open set, U, in G and there are functions, f simultaneously in every Lr(G), p≤r ≤∞, and g simultaneously in every Lq(G), 1 ≤q≤∞, such that the convolution, f * g(y), is not defined for any y in U.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 2 , June 1971 , pp. 265 - 266
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Rickert, N. W., Convolution of Lp functions, Proc. Amer. Math. Soc. 18 (1967), 762-763.Google Scholar
2. Zelazko, W., A note on Lp-algebras, Colloq. Math. 10 (1963), 53-56.Google Scholar