On the Lebesgue Summability of Multiple Trigonometric Series

Authors

  • Mónika Bagota Teacher’s Training College, University of Szeged, Szeged, Hungary
  • Ferenc Móricz Bolyai Institute, University of Szeged, Szeged, Hungary

DOI:

https://doi.org/10.5644/SJM.05.2.09

Keywords:

Formal integration of multiple trigonometric series, symmetric derivative and its extension to functions in several variables, Lebesgue method of summability

Abstract

The Lebesgue summability of a trigonometric series is defined in terms of the symmetric differentiability of the sum of the formally integrated trigonometric series in question. In this paper we extend the theorems of Fatou and Zygmund from single to multiple trigonometric series.

 

2000 Mathematics Subject Classification. 42A24, 42B08

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References

P. Fatou, S´eries trigonom´etriques et s´eries de Taylor, Acta Math., 30 (1906), 335–400.

M. Bagota and F. M´oricz, On the Lebesgue summability of double trigonometric series, J. Math. Anal. Appl., 348 (2008), 555–561.

A. Zygmund, Trigonometric Series, Vol. I., Cambridge Univ. Press, 1959.

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Published

11.06.2024

How to Cite

Bagota, M., & Móricz, F. (2024). On the Lebesgue Summability of Multiple Trigonometric Series. Sarajevo Journal of Mathematics, 5(2), 257–267. https://doi.org/10.5644/SJM.05.2.09

Issue

Vol. 5 No. 2 (2009)

Section

Articles