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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2021 Volume 200, Pages 73–80 (Mi into902)

This article is cited in 1 paper

Estimates for the rate of convergence of Fourier series in the Sobolev orthogonal functional system generated by the Walsh system

M. G. Magomed-Kasumov

Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala

Abstract: 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.

UDC: 517.521

MSC: 41A25,41A30

DOI: 10.36535/0233-6723-2021-200-73-80



© Steklov Math. Inst. of RAS, 2025