Abstract
We study the rate of Lp approximation by Ces⦏ro means of the quadratic partial sums of double Walsh-Fourier series of functions from Lp.
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Fine, N.J., Cesàro Summability of Walsh-Fourier Series, Proc. Nat. Acad. Sci. U.S.A., 41(1955), 558–591.
Glukhov, V.A., On the Summability of Multiple Fourier Series with respect to Multiplicative Systems (Russian), Mat. Zamet., 39(1986), 665–673.
Golubov, B.I., Efimov, A.V. and Skvortsov, V.A., Series and Transformations of Walsh, Nauka, Moscov, 1987 (Russian); English Transl.: Kluwer Acad. Publ; 1991.
Goginava, U., Convergence and Summability of Multiple Fourier-Walsh Series inL p([0, 1]N) Metrics, Bull. of Georgian Acad. Sci., 158(1998), 11–13.
Goginava, U., On the Convergence and Summability ofN-Dimensional Fourier Series with respect to the Walsh-Paley Systems in the SpacesL p([0, 1]N),p∈[1, ∞], Georgian Math. J., 7(2000), 53–72.
Goginava, U., On the Uniform Summability of Multiple Walsh-Fourier Series. Anal. Math., 26(2000), 209–226.
Goginava, U., On the Approximation Properties of Cesàro Means of Negative Order of Walsh-Fourier Series. J. Approx. Theory, 115(2002), 9–20.
Paley, A., A Remarkable Series of Orthogonal Functions, Proc. London Math. Soc., 34(1932), 241–279.
Schipp, F., Wade, W., Simon, P. and Pàl, J., Walsh Series, Introduction to Dyadic Harmonic Analysis, Adam Hilger, Briston and New York, 1990.
Schipp, F., Uber Gewiessen Maximaloperatoren, Annales Univ. Sci. Budapestiensis, Secto Math., 18(1975), 189–195.
Tevzadze, V.I., Uniform Convergence of Cesàro Means of Negative Order of Fourier Walsh Series (Russian) Soobshch. Acad. Nauk Gruzin. SSR 102(1981), 33–36.
Zhizhiashvili, L.V., Trigonometric Fourier Series and their Conjugates, Tbilisi, 1993 (Russian); English Transl.: Kluwer Acad. Publ; 1996.
Zygmund, A., Trigonometric Series, Vol. 1, Cambridge Univ. Press, 1959.
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Goginava, U. Approximation properties of (C, α) means of double walsh-Fourier series. Anal. Theory Appl. 20, 77–98 (2004). https://doi.org/10.1007/BF02835261
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DOI: https://doi.org/10.1007/BF02835261