Abstract
In 1987 Harris proved-among others that for each 1 ≤ p < 2 there exists a two-dimensional function f ∈ Lp such that its triangular Walsh-Fourier series does not converge almost everywhere. In this paper we prove that the set of the functions from the space Lp(II2) (1 ≤ p < 2) with subsequence of triangular partial means \(S_{2^A}^\Delta(f)\) of the double Walsh-Fourier series convergent in measure on II2 is of first Baire category in Lp(II2). We also prove that for each function f ∈ L2(II2) a.e. convergence \(S_{a(n)}^\Delta (f) \rightarrow f\) holds, where a(n) is a lacunary sequence of positive integers.
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The authors would like to thank the referee for providing extremely useful suggestions and corrections that improved the content of this paper.
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Russian Text © The Author(s), 2019, published in Izvestiya Natsional’noi Akademii Nauk Armenii, Matematika, 2019, No. 4, pp. 3–11.
The research was supported by the Hungarian National Foundation for Scientific Research (OTKA), grant no. K.111651
The research was supported by Shota Rustaveli National Science Foundation grant 217282
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Gát, G., Goginava, U. Convergence of a Subsequence of Triangular Partial Sums of Double Walsh-Fourier Series. J. Contemp. Mathemat. Anal. 54, 210–215 (2019). https://doi.org/10.3103/S1068362319040034
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DOI: https://doi.org/10.3103/S1068362319040034