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Convergence and localization of multiple Fourier series for classes of bounded Λ-variation

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Abstract

Previously obtained results for convergence and localization of multiple trigonometric Fourier series for functions from classes of bounded Λ-variation and embedding of these classes into each other are strengthened in the paper. The case when sequences Λ and M have a limit of the ratio Σ N n=1 1/λ n /Σ N n=1 1/µ n is considered. A more strict condition, the existence of a limit for the ratio λ n /µ n was considered before.

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    A. N. Bakhvalov

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  1. A. N. Bakhvalov
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Original Russian Text © A.N. Bakhvalov, 2008, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2008, Vol. 63, No. 3, pp. 6–12.

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Bakhvalov, A.N. Convergence and localization of multiple Fourier series for classes of bounded Λ-variation. Moscow Univ. Math. Bull. 63, 85–91 (2008). https://doi.org/10.3103/S0027132208030017

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  • DOI: https://doi.org/10.3103/S0027132208030017

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