Singular measures with absolutely continuous convolution squares on locally compact groups

Abstract

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