This is an announcement for the paper "On uniformly bounded basis in spaces of holomorphic functions" by Jean Bourgain. Abstract: The main result of the paper is the construction of explicit uniformly bounded basis in the spaces of complex homogenous polynomials on the unit ball of $C^3$, extending an earlier result of the author in the $C^2$ case Archive classification: math.FA Mathematics Subject Classification: Primary: 46E15, 32A99 Secondary: 42A56 Submitted from: bourgain@ias.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1506.05694 or http://arXiv.org/abs/1506.05694