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 Lobachevskii J. Math., 2002, Volume 11, Pages 7–12 (Mi ljm114)

On the coefficient multipliers theorem of Hardy and Littlewood

a Kazan State University
b Technische Universität Braunschweig, Institut für Analysis und Algebra

Abstract: Let $a_n(f)$ be the Taylor coefficients of a holomorphic function $f$ which belongs to the Hardy space $H^p$, $0<p<1$. We prove the estimate $C(p)\leq\pi\epsilon^p/[p(1-p)]$ in the Hardy-Littlewood inequality
$$\sum_{n=0}^\infty\frac{|a_n(f)|^p}{(n+1)^{2-p}}\leq C(p)(\| f \|_p)^p.$$
We also give explicit estimates for sums $\sum|a_n(f)\lambda_n|^s$ the mixed norm space $H(1,s,\beta)$. In this way we obtain a new version of some results by Blasco and by Jevtič and Pavlovič.

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Citation: F. G. Avkhadiev, K.-J. Wirths, “On the coefficient multipliers theorem of Hardy and Littlewood”, Lobachevskii J. Math., 11 (2002), 7–12

Citation in format AMSBIB
\Bibitem{AvkWir02} \by F.~G.~Avkhadiev, K.-J.~Wirths \paper On the coefficient multipliers theorem of Hardy and Littlewood \jour Lobachevskii J. Math. \yr 2002 \vol 11 \pages 7--12 \mathnet{http://mi.mathnet.ru/ljm114} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1946352} \zmath{https://zbmath.org/?q=an:1032.46037}