This is an announcement for the paper "Maximal theorems and square functions for analytic operators on Lp-spaces" by Christian Le Merdy and Quanhua Xu. Abstract: Let T : Lp --> Lp be a contraction, with p strictly between 1 and infinity, and assume that T is analytic, that is, there exists a constant K such that n\norm{T^n-T^{n-1}} < K for any positive integer n. Under the assumption that T is positive (or contractively regular), we establish the boundedness of various Littlewood-Paley square functions associated with T. As a consequence we show maximal inequalities of the form $\norm{\sup_{n\geq 0}\, (n+1)^m\bigl\vert T^n(T-I)^m(x) \bigr\vert}_p\,\lesssim\, \norm{x}_p$, for any nonnegative integer m. We prove similar results in the context of noncommutative Lp-spaces. We also give analogs of these maximal inequalities for bounded analytic semigroups, as well as applications to R-boundedness properties. Archive classification: math.FA math.OA Mathematics Subject Classification: 47B38, 46L52, 46A60 Submitted from: clemerdy@univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1011.1360 or http://arXiv.org/abs/1011.1360