Geodesic
Some summability methods for power series of functions in $H^p(D^n)$, $0$
Sbornik. Mathematics, Tome 200 (2009) no. 2, pp. 243-260 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $H^p(D^n)$ be a Hardy space in the unit polydisc $$ D^n=\{z\in\mathbb C^n:|z_j|<1,\,j=1,\dots,n\} $$ and let $$ R^{l,\alpha}_\varepsilon(f,e^{i\theta})=\sum_k(1-(\varepsilon|k|)^l)^\alpha_+\widehat f_ke^{ik\theta}, \qquad l>0, \quad \alpha>0, $$ be the generalized Riesz means of a function $f\in H^p(D^n)$. For certain standard relations between $p$, $l$, $n$ and $\alpha$ the following estimate is established: $$ C_1(\alpha,l,p)\widetilde{\omega}_l(\varepsilon,f)_p \le\bigl\|f(e^{i\theta})-R_\varepsilon^{l,\alpha}(f,e^{i\theta})\bigr\|_p \le C_2(\alpha,l,p)\omega_l(\varepsilon,f)_p, $$ where $\widetilde\omega_l(\varepsilon,f)_p$ and $\omega_l(\varepsilon,f)_p$ are integral moduli of continuity of order $l$. Bibliography: 13 titles.
Keywords: series' means, generalized Riesz means, generalized Abel-Poisson means, right fractional Riemann-Liouville integral, right fractional derivative. 
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S. G. Pribegin. Some summability methods for power series of functions in $H^p(D^n)$, $0

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