This is an announcement for the paper "Moduli of convexity and smoothness of reflexive subspaces of L^1" by S. Lajara, A. Pallares and S. Troyanski. Abstract: We show that for any probability measure \mu there exists an equivalent norm on the space L^1(\mu) whose restriction to each reflexive subspace is uniformly smooth and uniformly convex, with modulus of convexity of power type 2. This renorming provides also an estimate for the corresponding modulus of smoothness of such subspaces. Archive classification: math.FA Mathematics Subject Classification: 46B03, 46B10, 46B20, 46B25 Submitted from: apall@um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1104.2802 or http://arXiv.org/abs/1104.2802