We give tight bounds on the degree $f_\ell$ homogenous parts of abounded function $f$ on the cube . We describe applications topseudorandomness and learning theory . We use similar methods to generalize theclassical Pisier’s inequality from convex analysis . Our analysis involvesproperties of real-rooted polynomials that may be useful elsewhere .

Author(s) : Siddharth Iyer, Anup Rao, Victor Reis, Thomas Rothvoss, Amir Yehudayoff