Abstract
In this paper, we first present the second-order Riesz and Nörlund logarithmic summation methods, followed by a class of regular summation techniques based on second-order logarithmic averages. We then examine their applications to the pointwise convergence of Fourier series for continuous and integrable functions.
References
[1] N. K. Bary, A Treatise on Trigonometric Series. Vols. I, The Macmillan, New York, 1964. Search in Google Scholar
[2] R. E. Edwards, Fourier Series. A Modern Introduction. Vol. 1, 2nd ed., Grad. Texts in Math. 64, Springer, New York, 1979. 10.1007/978-1-4612-6208-4_1Search in Google Scholar
[3] G. Gát and K. Nagy, On the logarithmic summability of Fourier series, Georgian Math. J. 18 (2011), no. 2, 237–248. 10.1515/gmj.2011.0023Search in Google Scholar
[4] U. Goginava and G. Tkebuchava, Convergence of the logarithmic means of Fourier series, J. Math. Anal. Approx. Theory 1 (2006), no. 1, 30–41. Search in Google Scholar
[5] G. H. Hardy and W. W. Rogosinski, Fourier Series, Cambridge Tracts Math. Math. Phys. 38, Cambridge University, Cambridge, 1956. Search in Google Scholar
[6] X. Z. Krasniqi, On the convergence (upper boundness) of trigonometric series, Math. Commun. 14 (2009), no. 2, 245–254. Search in Google Scholar
[7]
X. Z. Krasniqi,
On a necessary condition for
[8]
X. Z. Krasniqi, P. Kórus and F. Móricz,
Necessary conditions for the
[9] F. Móricz, On the harmonic averages of numerical sequences, Arch. Math. (Basel) 86 (2006), no. 4, 375–384. 10.1007/s00013-005-1588-3Search in Google Scholar
[10] O. Szász, On the logarithmic means of rearranged partial sums of a Fourier series, Bull. Amer. Math. Soc. 48 (1942), 705–711. 10.1090/S0002-9904-1942-07763-9Search in Google Scholar
[11] G. Tkebuchava, Logarithmic summability of Fourier series, Acta Math. Acad. Paedagog. Nyházi 21 (2005), no. 2, 161–167. Search in Google Scholar
[12] K. Yabuta, Quasi-Tauberian theorems, applied to the summability of Fourier series by Riesz’s logarithmic means, Tohoku Math. J. (2) 22 (1970), 117–129. 10.2748/tmj/1178242866Search in Google Scholar
[13] A. Zigmund, Trigonometric Series. Vol. 1, Cambridge University, Canbridge, 1959. Search in Google Scholar
© 2025 Walter de Gruyter GmbH, Berlin/Boston