Abstract
It is well-known that if an one-dimensional function is continuously differentiable on [0, 1], then its Fourier-Haar series converges absolutely. On the other hand, if a function of two variables has continuous partial derivatives f ′ x and f ′ y on T 2, then its Fourier series does not necessarily absolutely converge with respect to a multiple Haar system (see [1]). In this paper we state sufficient conditions for the absolute convergence of the Fourier-Haar series for two-dimensional continuously differentiable functions.
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Original Russian Text © L.D. Gogoladze and V.Sh. Tsagareishvili, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2008, No. 5, pp. 14–25.
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Gogoladze, L.D., Tsagareishvili, V.S. The absolute convergence of the Fourier-Haar series for two-dimensional functions. Russ Math. 52, 9–19 (2008). https://doi.org/10.3103/S1066369X08050022
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DOI: https://doi.org/10.3103/S1066369X08050022