Some inequalities for Franklin series

Некоторые неравенст ва для рядов по систем е Франклина

Abstract

Обозначим через {f _k (t)} ^∞_k=0 систему Франклина на отрезке [0, 1]. Доказано, чт о еслиg∈L(0,1), то

$$mes\{ t:|\sum\limits_{\kappa = 0}^\infty {\varepsilon _\kappa a_\kappa (g)f_\kappa (t)| > y} \} \leqq \frac{B}{y}\int\limits_0^1 {|g(t)|dt} $$

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МАТЕМАТИЧЕСК ИЙ ИНСТИТУТ, ИМ. В. А. СТЕ КЛОВА АН СССР, УЛ. ВАВ ИЛОВА 42, 117333, МОСКВА, СССР
С. В. Бочкарев

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С. В. Бочкарев
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Бочкарев, С.В. Some inequalities for Franklin series. Analysis Mathematica 1, 249–257 (1975). https://doi.org/10.1007/BF02333175

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