Abstract
The paper deals with the question of convergence of multiple Fourier-Haar series with partial sums taken over homothetic copies of a given convex bounded set \(W\subset\mathbb{R}_+^n\) containing the intersection of some neighborhood of the origin with \(\mathbb{R}_+^n\). It is proved that for this type sets W with symmetric structure it is guaranteed almost everywhere convergence of Fourier-Haar series of any function from the class L(ln+L)n−1.
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Russian Text © The Author(s), 2019, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2019, No. 5, pp. 70–81.
The research is supported by Shota Rustaveli National Science Foundation (project no. 217282).
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Oniani, G.G., Tulone, F. On the Almost Everywhere Convergence of Multiple Fourier-Haar Series. J. Contemp. Mathemat. Anal. 54, 288–295 (2019). https://doi.org/10.3103/S1068362319050054
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DOI: https://doi.org/10.3103/S1068362319050054