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Convolution of Lp Functions on Non-Unimodular Groups
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1971
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