Asymptotically best possible Lebesque-type inequalities for the Fourier sums on sets of generalized Poisson integrals
| Autor: | Serdyuk, Anatoly, Stepaniuk, Tetiana |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | In this paper we establish Lebesgue-type inequalities for $2\pi$-periodic functions $f$, which are defined by generalized Poisson integrals of the functions $\varphi$ from $L_{p}$, $1\leq p< \infty$. In these inequalities uniform norms of deviations of Fourier sums $\| f-S_{n-1} \|_{C}$ are expressed via best approximations $E_{n}(\varphi)_{L_{p}}$ of functions $\varphi$ by trigonometric polynomials in the metric of space $L_{p}$. We show that obtained estimates are asymptotically best possible. Comment: 15 pages |
| Databáze: | arXiv |
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