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arXiv · 2509.15769

Estimates of deviations of Fourier sums on Weyl-Nagy classes $W^r_{\beta,1}$

A. S. Serdyuk·I. V. Sokolenko
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Abstract

We establish estimates for exact upper bounds of deviations of partial Fourier sums $S_{n-1}(f)$ on classes $W^r_{\beta,1}, r>2, \beta\in\mathbb{R},$ of $2\pi$-periodic functions whose $(r,\beta)$-derivatives in the Weyl--Nagy sense belong to the unit ball of the space $L_1$. The specified estimates allow us to write asymptotic equalities for the quantities $\sup\limits_{f\in W^r_{\beta,1}}|f(x)-S_{n-1}(f;x)|$ as $n\rightarrow\infty$, $r\rightarrow\infty$ for arbitrary relations between the parameters $r$ and $n$.

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BibTeXRIS

A. S. Serdyuk, I. V. Sokolenko. 2025-09-19. Estimates of deviations of Fourier sums on Weyl-Nagy classes $W^r_{\beta,1}$. https://arxiv.org/abs/2509.15769

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