Summability of multiple Fourier series for functions of bounded generalized variation
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Orthogonal series, approximation theory, and related problems, Tome 280 (2013), pp. 150-161.

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U. Goginava; A. Sahakian. Summability of multiple Fourier series for functions of bounded generalized variation. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Orthogonal series, approximation theory, and related problems, Tome 280 (2013), pp. 150-161. http://geodesic.mathdoc.fr/item/TM_2013_280_a8/

[1] Bakhvalov A.N., “Nepreryvnost po $\Lambda $-variatsii funktsii mnogikh peremennykh i skhodimost kratnykh ryadov Fure”, Mat. sb., 193:12 (2002), 3–20 | DOI | MR | Zbl

[2] Bakhvalov A.N., “Summirovanie metodami Chezaro ryadov Fure funktsii iz mnogomernykh klassov Vatermana”, DAN, 437:6 (2011), 731–733 | MR | Zbl

[3] Chanturiya Z.A., “Modul izmeneniya funktsii i ego primenenie v teorii ryadov Fure”, DAN SSSR, 214:1 (1974), 63–66 | Zbl

[4] Dyachenko M.I., “Waterman Classes and Spherical Partial Sums of Double Fourier Series”, Anal. math., 21 (1995), 3–21 | DOI | MR | Zbl

[5] Dyachenko M.I., “Dvumernye klassy Vatermana i $u$-skhodimost ryadov Fure”, Mat. sb., 190:7 (1999), 23–40 | DOI | MR | Zbl

[6] Dyachenko M.I.; Waterman D., “Convergence of double Fourier series and $W$-classes”, Trans. Amer. Math. Soc., 357 (2005), 397–407 | DOI | MR | Zbl

[7] Goginava U., “On the uniform convergence of multiple trigonometric Fourier series”, East J. Approx., 5:3 (1999), 253–266 | MR | Zbl

[8] Goginava U., “On the uniform summability of two-dimensional trigonometric Fourier series”, Proc. A. Razmadze Math. Inst., 124 (2000), 55–72 | MR | Zbl

[9] Goginava U., “Uniform convergence of Cesàro means of negative order of double Walsh–Fourier series”, J. Approx. Theory, 124:1 (2003), 96–108 | DOI | MR | Zbl

[10] Goginava U., “Uniform convergence of Cesàro means of negative order of double trigonometric Fourier series”, Anal. Theory Appl., 23:3 (2007), 255–265 | DOI | MR | Zbl

[11] Goginava U., Sahakian A., “On the convergence of double Fourier series of functions of bounded partial generalized variation”, East J. Approx, 16:2 (2010), 153–165 | MR

[12] Hardy G.H., “On double Fourier series, and especially those which represent the double zeta-function with real and incommensurable parameters”, Q. J. Pure Appl. Math., 37 (1906), 53–79

[13] Jordan C., “Sur la série de Fourier”, C. r. Acad. sci. Paris, 92 (1881), 228–230

[14] Marcinkiewicz J., “On a class of functions and their Fourier series”, C. r. Soc. sci. Warsowie, 26 (1934), 71–77 | Zbl

[15] Sablin A.I., “$\Lambda $-variatsiya i ryady Fure”, Izv. vuzov. Matematika, 1987, no. 10, 66–68 | MR | Zbl

[16] Saakyan A.A., “O skhodimosti dvoinykh ryadov Fure funktsii ogranichennoi garmonicheskoi variatsii”, Izv. AN ArmSSR. Ser. mat., 21:6 (1986), 517–529 | MR

[17] Waterman D., “On convergence of Fourier series of functions of generalized bounded variation”, Stud. math., 44 (1972), 107–117 | MR | Zbl

[18] Waterman D., “On the summability of Fourier series of functions of $\Lambda $-bounded variation”, Stud. math., 55 (1976), 87–95 | MR | Zbl

[19] Wiener N., “The quadratic variation of a function and its Fourier coefficients”, Mass. J. Math., 3 (1924), 72–94 | Zbl

[20] Zhizhiashvili L., Trigonometric Fourier series and their conjugates, Kluwer, Dordrecht, 1996 | MR | Zbl

[21] Zigmund A., Trigonometricheskie ryady, T. 1, Mir, M., 1965 | MR