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Matematicheskie Zametki, 2024, Volume 115, Issue 2, Pages 286–297
DOI: https://doi.org/10.4213/mzm13976 (Mi mzm13976) 		 
Estimate for the Rate of Uniform Convergence of the Fourier Series of a Continuous Periodic Function of Bounded $p$-Variation

T. Yu. Semenovaab

a Lomonosov Moscow State University
b Moscow Center for Fundamental and Applied Mathematics
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DOI: https://doi.org/10.4213/mzm13976
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.
Keywords: function of bounded $p$-variation, convergence rate of Fourier series.
Received: 07.04.2023
Revised: 15.07.2023
English version:
Mathematical Notes, 2024, Volume 115, Issue 2, Pages 258–268
DOI: https://doi.org/10.1134/S0001434624010243
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: 26
Language: Russian
Citation: T. Yu. Semenova, “Estimate for the Rate of Uniform Convergence of the Fourier Series of a Continuous Periodic Function of Bounded $p$-Variation”, Mat. Zametki, 115:2 (2024), 286–297; Math. Notes, 115:2 (2024), 258–268
Citation in format AMSBIB
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\by T.~Yu.~Semenova
\paper Estimate for the Rate of Uniform Convergence of the Fourier Series of a Continuous Periodic Function of Bounded~$p$-Variation
\jour Mat. Zametki
\yr 2024
\vol 115
\issue 2
\pages 286--297
\mathnet{http://mi.mathnet.ru/mzm13976}
\crossref{https://doi.org/10.4213/mzm13976}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4734360}
\transl
\jour Math. Notes
\yr 2024
\vol 115
\issue 2
\pages 258--268
\crossref{https://doi.org/10.1134/S0001434624010243}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85190884153}
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