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On the degree of convergence of Borel and Euler means for double Fourier series of functions of bounded variation in Hardy sense. (English) Zbl 0849.42009
The author considers a function \(f(x, y)\) which is periodic in each variable and is of bounded variation in the sense of Hardy. As is known, the rectangular partial sums of the double Fourier series of such an \(f\) converge at each point. Now, the present author estimates the rate of this convergence as well as the convergence rate of summation by Borel and Euler means.
Theorem 1 was proved by the reviewer [J. Approximation Theory 71, No. 3, 344-358 (1992; Zbl 0758.42004)].
Reviewer: F.Móricz (Szeged)
MSC:
42B08 Summability in several variables
42B05 Fourier series and coefficients in several variables
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