%0 Journal Article
%T A good universal weight for multiple recurrence averages with commuting transformations in norm
%A Idris Assani
%A Ryo Moore
%J Mathematics
%D 2015
%I arXiv
%X We will show that the sequences appearing in Bourgain's double recurrence result are good universal weights to the multiple recurrence averages with commuting measure-preserving transformations in norm. This will extend the pointwise converge result of Bourgain, the norm convergence result of Tao, and the authors' previous work on the single measure-preserving transformation. The proof will use the double-recurrence Wiener-Wintner theorem, factor decompositions (Host-Kra-Ziegler factors), nilsequences, and various seminorms including the ones by Gowers-Host-Kra as well as the box seminorms introduced by Host.
%U http://arxiv.org/abs/1506.06730v2