2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58493In a recent paper of Wolff the optimal decay of circular L^p means of compactly supported measures of finite energy was given for p>=2, with application to Falconer's distance problem. The question was then raised in that paper as to whether any non-trivial improvement to these estimates were available for p < 2. We answer this question in the negative.The proof of the main result in this paper is incorrect, and this paper has been withdrawnClassical Analysis and ODEs42B10, 28A75text