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Lebesgue-type inequalities for the Fourier sums on classes of generalized Poisson integrals

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Serdyuk A. S., Stepanyuk T. A.
Bulletin de la Société des Sciences et des Lettres de Łódź, Série: Recherches sur les déformations
|
2018
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vol. 68
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issue 2
45-52
PL
https://doi.org/10.26485/0459-6854/2018/68.2/4 Dla funkcji ze zbioru uogólnionych całek Poissona otrzymujemy górne oszacowanie dla odchyleń sum Fouriera w jednostajnej metryce w terminach najlepszej aproksymacji uogólnionych pochodnych  funkcji tego typu w metryce przestrzeni. Uzyskane oszacowania są asymptotycznie najlepsze z możliwych.
EN
https://doi.org/10.26485/0459-6854/2018/68.2/4 For functions from the set of generalized Poisson integrals  , we obtain upper estimates for the deviations of Fourier sums in the uniform metric in terms of the best approximations of the generalized derivatives  of functions of this kind by trigonometric polynomials in the metric of the spaces . Obtained estimates are asymptotically best possible.
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