2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159820More work needs to be done to move from the tail to the averages themselves. So at this time we prefer to withdraw the paper about the averages. However a previous version of the paper which deals with the tail has been checked and we believe it to be complete and correct.This paper has been withdrawnDynamical SystemsClassical Analysis and ODEs37A05 (Primary); 37A50, 28D05 (Secondary)The $(L^{p},L^{1})$ bilinear Hardy-Littlewood function and Furstenberg averagestext