Geodesic
Estimate for the Rate of Uniform Convergence of the Fourier Series of a Continuous Periodic Function of Bounded~$p$-Variation
Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 286-297

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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. 
@article{MZM_2024_115_2_a11,
     author = {T. Yu. Semenova},
     title = {Estimate for the {Rate} of {Uniform} {Convergence} of the {Fourier} {Series} of a {Continuous} {Periodic} {Function} of {Bounded~}$p${-Variation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {286--297},
     publisher = {mathdoc},
     volume = {115},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a11/}
}
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T. Yu. Semenova. Estimate for the Rate of Uniform Convergence of the Fourier Series of a Continuous Periodic Function of Bounded~$p$-Variation. Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 286-297. http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a11/