This is an announcement for the paper "Vector-valued Littlewood-Paley-Stein theory for semigroups" by Teresa Martinez, Jose L. Torrea and Quanhua Xu. Abstract: We develop a generalized Littlewood-Paley theory for semigroups acting on $L^p$-spaces of functions with values in uniformly convex or smooth Banach spaces. We characterize, in the vector-valued setting, the validity of the one-sided inequalities concerning the generalized Littlewood-Paley-Stein $g$-function associated with a subordinated Poisson symmetric diffusion semigroup by the martingale cotype and type properties of the underlying Banach space. We show that in the case of the usual Poisson semigroup and the Poisson semigroup subordinated to the Ornstein-Uhlenbeck semigroup on ${\mathbb R}^n$, this general theory becomes more satisfactory (and easier to be handled) in virtue of the theory of vector-valued Calder\'on-Zygmund singular integral operators. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20; 42B25, 42A61 Remarks: To appear in Adv. Math The source file(s), lpsII.tex: 111765 bytes, is(are) stored in gzipped form as 0505303.gz with size 31kb. The corresponding postcript file has gzipped size 144kb. Submitted from: qx@math.univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0505303 or http://arXiv.org/abs/math.FA/0505303 or by email in unzipped form by transmitting an empty message with subject line uget 0505303 or in gzipped form by using subject line get 0505303 to: math@arXiv.org.