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.
Keywordsfunctions of bounded variation in two variables Fourier coefficients Parseval’s identity
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- 2.S. A. Telyakovskii, “On partial sums of Fourier series of functions of bounded variation,” in Trudy Mat. Inst. Steklov, Vol. 219: Theory of Approximations. Harmonic Analysis (Nauka, Moscow, 1997), pp. 378–386 [Proc. Steklov Inst.Math. 219, 372–381 (1997)].Google Scholar