On the coefficient multipliers theorem of Hardy and Littlewood
(Lobachevskii Journal of Mathematics, Volume XI)
Let an(f) be the Taylor coefficients of a holomorphic function f which belongs to the Hardy space Hp. We prove the estimate C(p)≤πep/[p(1-p)] in the Hardy-Littlewood inequality
We also give explicit estimates for sums 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.