## F. G. Avkhadiev, K.-J. Wirths

## On the coefficient multipliers theorem of Hardy and Littlewood

## (Lobachevskii Journal of Mathematics, Vol.11, pp.7-12)

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)\le\pi e^p/[p(1-p)] in the Hardy-Littlewood inequality
/BR
\sum_{n=0}^\infty \frac{|a_n(f)|^p}{(n+1)^{2-p}}\le C(p)(\| f\|_p)^p.
/BR
We also give explicit estimates for sums \sum|a_n(f)\lambda_n|^s
in the mixed norm space H(1,s,\beta).
In this way we obtain a new version of
some results by Blasco and by Jevti\u{c} and Pavlovi\u{c}.

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