On the coefficient multipliers theorem of Hardy and Littlewood

Abstract

Let an(f) be the Taylor coefficients of a holomorphic function f which belongs to the Hardy space Hp, 0 < p < 1. We prove the estimate C(p) ≤ πep/[p(1 - p)] in the Hardy-Littlewood inequality We also give explicit estimates for sums Σ|a n(f)λn|s in the mixed norm space H(1, s, β). In this way we obtain a new version of some results by Blasco and by Jevtič and Pavlovič.