Geodesic
On the coefficient multipliers theorem of Hardy and Littlewood
Lobachevskii journal of mathematics, Tome 11 (2002), pp. 7-12

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Let $a_n(f)$ be the Taylor coefficients of a holomorphic function $f$ which belongs to the Hardy space $H^p$, $0$. 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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     author = {F. G. Avkhadiev and K.-J. Wirths},
     title = {On the coefficient multipliers theorem of {Hardy} and {Littlewood}},
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     publisher = {mathdoc},
     volume = {11},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2002_11_a1/}
}
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F. G. Avkhadiev; K.-J. Wirths. On the coefficient multipliers theorem of Hardy and Littlewood. Lobachevskii journal of mathematics, Tome 11 (2002), pp. 7-12. http://geodesic.mathdoc.fr/item/LJM_2002_11_a1/