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 Mat. Zametki, 1973, Volume 14, Issue 5, Pages 615–626 (Mi mz9946)

Points of strong summability of Fourier series

O. D. Gabisoniya

Sukhumskii Pedagogic Institute

Abstract: In this paper we present a new solution of Hardy and Littlewood's problem concerning strong summability of Fourier series; we also present a property of points of strong summability.

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English version:
Mathematical Notes, 1973, 14:5, 913–918

Bibliographic databases:

UDC: 517.5

Citation: O. D. Gabisoniya, “Points of strong summability of Fourier series”, Mat. Zametki, 14:5 (1973), 615–626; Math. Notes, 14:5 (1973), 913–918

Citation in format AMSBIB
\Bibitem{Gab73} \by O.~D.~Gabisoniya \paper Points of strong summability of Fourier series \jour Mat. Zametki \yr 1973 \vol 14 \issue 5 \pages 615--626 \mathnet{http://mi.mathnet.ru/mz9946} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=330893} \zmath{https://zbmath.org/?q=an:0293.42003} \transl \jour Math. Notes \yr 1973 \vol 14 \issue 5 \pages 913--918 \crossref{https://doi.org/10.1007/BF01462249} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. M. I. Dyachenko, “Some problems in the theory of multiple trigonometric series”, Russian Math. Surveys, 47:5 (1992), 103–171
2. V. A. Rodin, “Extensions of a Certain Weak Type Operator”, Funct. Anal. Appl., 27:1 (1993), 70–73
3. V. A. Rodin, “Strong means and the oscillation of multiple Fourier–Walsh series”, Math. Notes, 56:3 (1994), 948–959
4. V. A. Rodin, “Strong means and oscillation of multiple Fourier series in multiplicative systems”, Math. Notes, 63:4 (1998), 533–541
5. R. A. Lasuriya, “$\varphi$-Strong Summability of Fourier–Laplace Series of Functions of Class $L(S^{m-1})$”, Math. Notes, 87:1 (2010), 138–140
6. Gat G., Goginava U., Karagulyan G., “Almost Everywhere Strong Summability of Marcinkiewicz Means of Double Walsh-Fourier Series”, Anal. Math., 40:4 (2014), 243–266
7. Goginava U., Gogoladze L., Karagulyan G., “Bmo-Estimation and Almost Everywhere Exponential Summability of Quadratic Partial Sums of Double Fourier Series”, Constr. Approx., 40:1 (2014), 105–120
8. Gat G., Goginava U., “Almost Everywhere Strong Summability of Double Walsh-Fourier Series”, J. Contemp. Math. Anal.-Armen. Aca., 50:1 (2015), 1–13
9. Lenski W. Szal B., “Pointwise Strong Approximation of Almost Periodic Functions in S-1”, Math. Inequal. Appl., 18:2 (2015), 735–750
10. Weisz F., “Convergence and Summability of Fourier Transforms and Hardy Spaces”, Convergence and Summability of Fourier Transforms and Hardy Spaces, Applied and Numerical Harmonic Analysis, Birkhauser Boston, 2017, 1–435
11. Goginava U., “Almost Everywhere Strong Summability of Cubic Partial Sums of D-Dimensional Walsh-Fourier Series”, Math. Inequal. Appl., 20:4 (2017), 1051–1066
12. U. Goginava, G. Karagulian, “On Exponential Summability of Rectangular Partial Sums of Double Trigonometric Fourier Series”, Math. Notes, 104:5 (2018), 655–665
13. Goginava U., “Almost Everywhere Convergence of Strong Norlund Logarithmic Means of Walsh-Fourier Series”, J. Contemp. Math. Anal.-Armen. Aca., 53:5 (2018), 281–287
14. Goginava U., “Almost Everywhere Strong C,1,0 Summability of 2-Dimensional Trigonometric Fourier Series”, Indian J. Pure Appl. Math., 51:3 (2020), 1181–1194
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