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Estimates for functionals by deviations of the Riesz sums in seminormed spaces

Authors:

N Yu Dodonov V V Zhuk

Institution:

(1) St. Petersburg State University, 28, Universitetskii pr., Petrodvorets, St. Petersburg, 198504, Russia

Abstract:

Suppose that (X, p) is a sermonized space, $\left\{ {xk} \right\}_{k = 0}^n$ is a linearly independent system of elements in X, $\left\{ {c_k } \right\}_{k = 0}^n$ is a sequence of linear bounded functionals such that c _k(x _l) = δ _kl,

$R_{n,r} (x) = \sum\limits_{k = 0}^n {\left( {1 - \left( {\frac{k}{n + 1}} \right)^r } \right)ck(x)x_k }$

are the Riesz sums. We prove general assertions concerning estimates from above for the values of semiadditive functionals $\Phi :X \to \mathbb{R}_{ + }$ by deviations of the Riesz sums p(x − R _n,r(x)). Bibliography: 6 titles. Dedicated to Nina Nikolaevna Uraltseva Translated from Problemy Matematicheskogo Analiza, 40, May 2009, pp. 57–68.

Keywords:

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