On the Convergence of Block Fourier Series of Functions of Bounded Variation in Two Variables


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We present a necessary and sufficient condition for the series of absolute values of blocks of Fourier series elements and blocks of series of summands in Parseval’s identity to converge in the class of two-variable functions of bounded variation in the sense of Hardy.

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S. Telyakovskii

Steklov Mathematical Institute of Russian Academy of Sciences; Lomonosov Moscow State University

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Email: satel@mi.ras.ru
俄罗斯联邦, Moscow; Moscow

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