Singular measures with absolutely continuous convolution squares on locally compact groups

Bisbas, Antonis

doi:10.1090/S0002-9939-99-04827-3

Singular measures with absolutely continuous convolution squares on locally compact groups
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Proc. Amer. Math. Soc. 127 (1999), 2865-2869 Request permission

Abstract:

Saeki’s result states that on any locally compact nondiscrete group there exist continuous singular measures, with respect to the left Haar measure, $\mu$ with $\mu * \mu$ in $L^{p}$ for all $p, \;1\leq p < \infty$. This paper gives a new and short proof of this using Rademacher-Riesz products.

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