The Hadamard product of polynomials in H0H0

We obtain sharp estimates for the Mahler measure of the Hadamard product of two polynomials. As a corollary, an estimate for the Hadamard product in Hardy spaces Hp(D)Hp(D), p∈(0,∞]p∈(0,∞], is obtained. We also give a simple proof of Bernstein’s inequality, and derive an estimate for the Mahler measure and the HpHp-pre-norm of the odd and even parts of a polynomial.