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arXiv · 1908.09517

Asymptotically best possible Lebesque-type inequalities for the Fourier sums on sets of generalized Poisson integrals

Anatoly Serdyuk·Tetiana Stepaniuk
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Abstract

In this paper we establish Lebesgue-type inequalities for $2π$-periodic functions $f$, which are defined by generalized Poisson integrals of the functions $φ$ 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 $E_{n}(φ)_{L_{p}}$ of functions $φ$ by trigonometric polynomials in the metric of space $L_{p}$. We show that obtained estimates are asymptotically best possible.

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Anatoly Serdyuk, Tetiana Stepaniuk. 2019-08-26. Asymptotically best possible Lebesque-type inequalities for the Fourier sums on sets of generalized Poisson integrals. https://arxiv.org/abs/1908.09517

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