Abstract
We obtain an estimate for the convergence rate of the Fourier series of a continuous periodic function in terms of the modulus of continuity of the function and the value of its \(p\)-variation. We prove that the leading term of the estimate is sharp.
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Acknowledgments
The author wishes to express deep gratitude to A. Yu. Popov for setting the problem and for the attention to the work.
Funding
This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
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Translated from Matematicheskie Zametki, 2024, Vol. 115, pp. 286–297 https://doi.org/10.4213/mzm13976.
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Semenova, T.Y. Estimate for the Rate of Uniform Convergence of the Fourier Series of a Continuous Periodic Function of Bounded \(p\)-Variation. Math Notes 115, 258–268 (2024). https://doi.org/10.1134/S0001434624010243
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DOI: https://doi.org/10.1134/S0001434624010243