Uniform summability of double Walsh-Fourier series of functions of bounded partial Λ-variation

[1] BAKHVALOV, A. N.: Continuity in Λ-variation of functions of several variables and the convergence of multiple Fourier series, Mat. Sb. 193 (2002), 3–20 (Russian) [English trans.: Sb. Math. 193, (2002), 1731–1748]. http://dx.doi.org/10.4213/sm69710.4213/sm697Search in Google Scholar

[2] CHANTURIA, Z. A.: The modulus of variation of a function and its application in the theory of Fourier series, Soviet. Math. Dokl. 15 (1974), 67–71. Search in Google Scholar

[3] DYACHENKO, M. I.: Waterman classes and spherical partial sums of double Fourier series, Anal. Math. 21 (1995), 3–21. http://dx.doi.org/10.1007/BF0190402210.1007/BF01904022Search in Google Scholar

[4] DYACHENKO, M. I.: Two-dimensional Waterman classes and u-convergence of Fourier series, Mat. Sb. 190 (1999), 23–40 (Russian) [English trans.: Sb. Math. 190 (1999), 955–972]. http://dx.doi.org/10.4213/sm41410.4213/sm414Search in Google Scholar

[5] DYACHENKO, M. I.— WATERMAN, D.: Convergence of double Fourier series and Wclasses, Trans. Amer. Math. Soc. 357 (2005), 397–407. http://dx.doi.org/10.1090/S0002-9947-04-03525-110.1090/S0002-9947-04-03525-1Search in Google Scholar

[6] GÁT, G.— GOGINAVA, U.— TKEBUCHAVA, G.: Convergence in measure of logarithmic means of quadratical partial sums of double Walsh-Fourier series, J. Math. Anal. Appl. 323 (2006), 535–549. http://dx.doi.org/10.1016/j.jmaa.2005.10.05610.1016/j.jmaa.2005.10.056Search in Google Scholar

[7] GÁT, G.— GOGINAVA, U.— NAGY, K.: On the Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system, Studia Sci. Math. Hungar. 46 (2009), 399–421. Search in Google Scholar

[8] GOGINAVA, U.: On the uniform convergence of multiple trigonometric Fourier series, East J. Approx. 3 (1999), 253–266. Search in Google Scholar

[9] GOGINAVA, U.: On the uniform convergence of Walsh-Fourier series, Acta Math. Hungar. 93 (2001), 59–70. http://dx.doi.org/10.1023/A:101386531568010.1023/A:1013865315680Search in Google Scholar

[10] GOGINAVA, U.: Uniform convergence of Cesàro means of negative order of double Walsh-Fourier series, J. Approx. Theory 124 (2003), 96–108. http://dx.doi.org/10.1016/S0021-9045(03)00134-510.1016/S0021-9045(03)00134-5Search in Google Scholar

[11] GOGINAVA, U.: Approximation properties of (C, α) means of double Walsh-Fourier series, Anal. Theory Appl. 20 (2004), 77–98. http://dx.doi.org/10.1007/BF0283526110.1007/BF02835261Search in Google Scholar

[12] GOGINAVA, U.: The weak type inequality for the maximal operator of the Marcinkiewicz-Fejér means of the two-dimensional Walsh-Fourier series, J. Approx. Theory 154 (2008), 161–180. http://dx.doi.org/10.1016/j.jat.2008.03.01210.1016/j.jat.2008.03.012Search in Google Scholar

[13] GOGINAVA, U.— SAHAKIAN A.: On the convergence of double Fourier series of functions of bounded partial generalized variation, East J. Approx. 16 (2010), 153–165. Search in Google Scholar

[14] GOGINAVA, U.— NAGY, K.: Boundedness of the maximal operators of double Walshlogarithmic means of Marcinkiewicz type, Math. Slovaca (To appear). Search in Google Scholar

[15] GOLUBOV, B. I.— EFIMOV, A. V.— SKVORTSOV. V. A.: Series and Transformations of Walsh, Nauka, Moscow, 1987 (Russian) [English trans.: Kluwer Academic, Dordrecht, 1991. Search in Google Scholar

[16] HARDY, G. H.: On double Fourier series and especially which represent the double zeta function with real and incommensurable parameters, Q. J. Math. 37 (1906), 53–79. Search in Google Scholar

[17] JORDAN, C.: Sur la series de Fourier, C. R. Acad. Sci. Paris 92 (1881), 228–230. Search in Google Scholar

[18] MARCINKIEWICZ, J.: On a class of functions and their Fourier series, Compt. Rend. Soc. Sci. Warsowie 26 (1934), 71–77. Search in Google Scholar

[19] MÓRICZ, F.: Rate of convergence for double Walsh-Fourier series of functions of bounded fluctuation, Arch. Math. (Basel) 60 (1993), 256–265. http://dx.doi.org/10.1007/BF0119881010.1007/BF01198810Search in Google Scholar

[20] MÓRICZ, F.: On the uniform convergence and L 1-convergence of double Walsh-Fourier series, Studia Math. 102 (1992), 225–237. 10.4064/sm-102-3-225-237Search in Google Scholar

[21] ONNEWEER, C. W.— WATERMAN, D.: Fourier series of functions of harmonic bounded fluctuation on groups, J. Anal. Math. 27 (1974), 79–83. http://dx.doi.org/10.1007/BF0278864310.1007/BF02788643Search in Google Scholar

[22] SABLIN, A. I.: Λ-variation and Fourier series, Izv. Vyssh. Uchebn. Zaved. Mat. 10 (1987), 66–68 (Russian) [English trans.: Russian Math. (Iz. VUZ) 31 (1987)]. Search in Google Scholar

[23] SAHAKIAN, A. A.: On the convergence of double Fourier series of functions of bounded harmonic variation, Izv. Nats. Akad. Nauk Armenii Mat. 21, (1986), 517–529 (Russian) [English trans.: J. Contemp. Math. Anal. 21, (1986), 1–13]. Search in Google Scholar

[24] SCHIPP, F.— WADE, W. R.— SIMON, P.— PÁL, J.: Walsh Series, an Introduction to Dyadic Harmonic Analysis, Adam Hilger, Bristol-New York, 1990. Search in Google Scholar

[25] WATERMAN, D.: On convergence of Fourier series of functions of generalized bounded variation, Studia Math. 44 (1972), 107–117. 10.4064/sm-44-2-107-117Search in Google Scholar

[26] WATERMAN, D.: On the summability of Fourier series of functions of Λ-bounded variation, Studia Math. 55 (1976), 87–95. 10.4064/sm-55-1-87-95Search in Google Scholar

[27] WIENER, N.: The quadratic variation of a function and its Fourier coefficients, Mass. J. Math. 3 (1924), 72–94. Search in Google Scholar

[28] ZYGMUND, A.: Trigonometric Series, Cambridge University Press, Cambridge, 1959. Search in Google Scholar