Geodesic
Estimates for the rate of convergence of Fourier series in the Sobolev orthogonal functional system generated by the Walsh system
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 2, Tome 200 (2021), pp. 73-80

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For functions from the Sobolev spaces $W^r_{L^p}$, we obtain several estimates for the rate of approximation by partial sums of Fourier series in Sobolev-type system generated by Walsh system: pointwise estimates; uniform estimates in terms of the integral modulus of continuity for the derivative; estimates in the metric of the Sobolev space $W^r_{L^p}$ in terms of the best approximations.
Keywords: Sobolev inner product, Walsh system, approximation properties, Sobolev space, Fourier series. 
@article{INTO_2021_200_a7,
     author = {M. G. Magomed-Kasumov},
     title = {Estimates for the rate of convergence of {Fourier} series in the {Sobolev} orthogonal functional system generated by the {Walsh} system},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {73--80},
     publisher = {mathdoc},
     volume = {200},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_200_a7/}
}
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M. G. Magomed-Kasumov. Estimates for the rate of convergence of Fourier series in the Sobolev orthogonal functional system generated by the Walsh system. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 20 International Saratov Winter School "Contemporary Problems of Function Theory and Their Applications", Saratov, January 28 — February 1, 2020. Part 2, Tome 200 (2021), pp. 73-80. http://geodesic.mathdoc.fr/item/INTO_2021_200_a7/