Convergence of a Subsequence of Triangular Partial Sums of Double Walsh-Fourier Series
- Авторы: Gát G.1, Goginava U.2
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Учреждения:
- University of Debrecen
- Tbilisi State University
- Выпуск: Том 54, № 4 (2019)
- Страницы: 210-215
- Раздел: Real and Complex Analysis
- URL: https://journals.rcsi.science/1068-3623/article/view/228344
- DOI: https://doi.org/10.3103/S1068362319040034
- ID: 228344
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Аннотация
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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Об авторах
G. Gát
University of Debrecen
Автор, ответственный за переписку.
Email: gat.gyorgy@science.unideb.hu
Венгрия, Debrecen
U. Goginava
Tbilisi State University
Автор, ответственный за переписку.
Email: zazagoginava@gmail.com
Грузия, Tbilisi