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  • 1 College of Nyíregyháza Institute of Mathematics and Computer Science P.O. Box 166 H-4400 Nyíregyháza Hungary
  • 2 Iv. Javakhishvili Tbilisi State University Department of Mathematics, Faculty of Exact and Natural Sciences Chavchavadze str. 1 0128 Tbilisi Georgia
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The maximal Orlicz spaces such that the mixed logarithmic means of multiple Walsh-Fourier series for the functions from these spaces converge in measure and in norm are found.

  • R. E. Edwards, Fourier series a modern introduction, vol. 1, Springer-Verlang, New-York, Heidelberg, Berlin 1982.

    Edwards R. E. , '', in Fourier series a modern introduction, vol. 1 , (1982 ) -.

  • Garsia, A., Topic in almost everywhere convergence, Chicago, 1970.

    Garsia A. , '', in Topic in almost everywhere convergence , (1970 ) -.

  • Gát, G., Investigation of certain operators with respect to the Vilenkin system, Acta Math. Hungar., 61 (1993), no. 1–2, 131–149.

    Gát G. , 'Investigation of certain operators with respect to the Vilenkin system ' (1993 ) 61 Acta Math. Hungar. : 131 -149.

    • Search Google Scholar
  • Gát, G., Goginava, U. and Tkebuchava, G., Convergence in measure of Logarithmic means of double Walsh-Fourier series, Georgian Math. J., 12 (2005), no. 4, 607–618.

    Tkebuchava G. , 'Convergence in measure of Logarithmic means of double Walsh-Fourier series ' (2005 ) 12 Georgian Math. J. : 607 -618.

    • Search Google Scholar
  • Gát, G., Goginava, U. and Tkebuchava, G., Convergence in measure of logarithmic means of quadratical partial sums of double Walsh-Fourier series, J. Math. Anal. Appl., 323 (2006), no. 1, 535–549.

    Tkebuchava G. , 'Convergence in measure of logarithmic means of quadratical partial sums of double Walsh-Fourier series ' (2006 ) 323 J. Math. Anal. Appl. : 535 -549.

    • Search Google Scholar
  • Gát, G., Goginava, U. and Tkebuchava, G., Convergence of logarithmic means of multiple Walsh-Fourier series, Anal. Theory Appl., 21 (2005), no. 4, 326–338.

    Tkebuchava G. , 'Convergence of logarithmic means of multiple Walsh-Fourier series ' (2005 ) 21 Anal. Theory Appl. : 326 -338.

    • Search Google Scholar
  • Gát, G., Goginava, U. and Nagy, K., On the Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system, Studia Sci. Math. Hungar., 46 (2009), no. 3, 399–421.

    Nagy K. , 'On the Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system ' (2009 ) 46 Studia Sci. Math. Hungar. : 399 -421.

    • Search Google Scholar
  • Gát, G. and Goginava, U., uniform and L-convergence of logarithmic means of Walsh-Fourier series, Acta Math. Sin. (Engl. Ser.), 22 (2006), no. 2, 497–506.

    Goginava U. , 'uniform and L-convergence of logarithmic means of Walsh-Fourier series ' (2006 ) 22 Acta Math. Sin. (Engl. Ser.) : 497 -506.

    • Search Google Scholar
  • 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), no. 2, 161–180.

    Goginava U. , 'The weak type inequality for the maximal operator of the Marcinkiewicz-Fejér means of the two-dimensional Walsh-Fourier series ' (2008 ) 154 J. Approx. Theory : 161 -180.

    • Search Google Scholar
  • Getsadze, R., On the divergence in measure of multiple Fourier series, Some problems of functions theory, 4 (1988), 84–117 (in Russian).

    Getsadze R. , 'On the divergence in measure of multiple Fourier series ' (1988 ) 4 Some problems of functions theory : 84 -117.

    • Search Google Scholar
  • Golubov, B. I., Efimov, A. V. and Skvortsov, V. A., Series and transformations of Walsh, Moscow, 1987 (Russian); English translation, Kluwer Academic, Dordrecht, 1991.

    Skvortsov V. A. , '', in Series and transformations of Walsh, Moscow, 1987 (Russian) , (1991 ) -.

    • Search Google Scholar
  • Krasnosel’skii, M. A. and Rutickii, Ya. B., Convex functions and Orlicz space (English translation), P. Noorhoff (Groningen, 1961).

    Rutickii Y.a. B. , '', in Convex functions and Orlicz space (English translation) , (1961 ) -.

  • Konyagin, S. V., Divergence with respect to measure of multiple Fourier series, (Russian) Mat. Zametki, 44 (1988), no. 2, 196–201, 286; translation in Math. Notes, 44 (1988), no. 1–2, 589–592 (1989).

    Konyagin S. V. , 'Divergence with respect to measure of multiple Fourier series, (Russian) ' (1988 ) 44 Mat. Zametki : 196 -201.

    • Search Google Scholar
  • Simon, P., Strong convergence of certain means with respect to the Walsh-Fourier series, Acta Math. Hungar., 49 (1987), 425–431.

    Simon P. , 'Strong convergence of certain means with respect to the Walsh-Fourier series ' (1987 ) 49 Acta Math. Hungar. : 425 -431.

    • Search Google Scholar
  • Schipp, F., Wade, W. R., Simon, P. and Pál, J., Walsh Series, an Introduction to Dyadic Harmonic Analysis, Adam Hilger, Bristol, New York, 1990.

    Pál J. , '', in Walsh Series, an Introduction to Dyadic Harmonic Analysis , (1990 ) -.

  • Szász, O., On the logarithmic means of rearranged partial sums of Fourier series, Bull. Amer. Math. Soc., 48 (1942), 705–711.

    Szász O. , 'On the logarithmic means of rearranged partial sums of Fourier series ' (1942 ) 48 Bull. Amer. Math. Soc. : 705 -711.

    • Search Google Scholar
  • Tkebuchava, G., Subsequences of partial sums of multiple Fourier and Fourier-Walsh series, Bull. Georgian Acad. Sci., 169 (2004), no. 2, 252–253.

    Tkebuchava G. , 'Subsequences of partial sums of multiple Fourier and Fourier-Walsh series ' (2004 ) 169 Bull. Georgian Acad. Sci : 252 -253.

    • Search Google Scholar
  • Yabuta, K., Quasi-Tauberian theorems, applied to the summability of Fourier series by Riesz’s logarithmic means, Tôhôku Math. Journ., 22 (1970), 117–129.

    Yabuta K. , 'Quasi-Tauberian theorems, applied to the summability of Fourier series by Riesz’s logarithmic means ' (1970 ) 22 Tôhôku Math. Journ. : 117 -129.

    • Search Google Scholar
  • Weisz, F., Strong convergence theorems for two-parameter Walsh- and trigonometric-Fourier series, Studia Math., 117 (1996), 173–194.

    Weisz F. , 'Strong convergence theorems for two-parameter Walsh- and trigonometric-Fourier series ' (1996 ) 117 Studia Math. : 173 -194.

    • Search Google Scholar
  • Zhizhiashvili, L. V., Some problems of multidimensional harmonic analysis, Tbilisi, TGU, 1996 (Russian).

    Zhizhiashvili L. V. , '', in Some problems of multidimensional harmonic analysis , (1996 ) -.

  • Zygmund, A., Trigonometric Series, vol. 1, Cambridge Univ. Press, Cambridge, 1959.

    Zygmund A. , '', in Trigonometric Series, vol. 1 , (1959 ) -.