# On the coefficient multipliers theorem of Hardy and Littlewood

## (*Lobachevskii Journal of Mathematics, Volume XI*)

Let a_{n}(f) be the Taylor coefficients of a holomorphic function f which belongs to the Hardy space H^{p}. We prove the estimate C(p)≤πe^{p}/[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.