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On the behavior of trigonometric series and power series


Authors: J. Marcinkiewicz and A. Zygmund
Journal: Trans. Amer. Math. Soc. 50 (1941), 407-453
MSC: Primary 42.4X
DOI: https://doi.org/10.1090/S0002-9947-1941-0005130-1
MathSciNet review: 0005130
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  • [1] A. F. Andersen Studier over Cesàro's Summabilitetsmetode, Copenhagen, Gjellerup, 1921.
  • [1] G. H. Hardy and J. E. Littlewood Contributions to the arithmetic theory of series, Proceedings of the London Mathematical Society, vol. 11 (1913), pp. 401-478.
  • [1] G. H. Hardy and M. Riesz Dirichlet's Series, Cambridge Tracts, Cambridge, 1915.
  • [1] J. Karamata, Über die Hardy-Littlewoodschen Umkehrungen des Abelschen Stetigkeitssatzes, Math. Z. 32 (1930), no. 1, 319–320 (German). MR 1545168, https://doi.org/10.1007/BF01194636
  • [1] E. Kogbetliantz Sommation des séries et intégrales divergentes, Mémorial des Sciences Mathématiques, vol. 51, pp. 1-75.
  • [1] B. Kuttner A theorem on trigonometric series, Journal of the London Mathematical Society, vol. 10 (1935), pp. 131-140.
  • [1] J. Marcinkiewicz, Sur la sommabilité forte de séries de Fourier, J. London Math. Soc. 14 (1939), 162–168 (French). MR 0000066, https://doi.org/10.1112/jlms/s1-14.3.162
  • [1] J. Marcinkiewicz and A. Zygmund On the differentiability of functions and summability of trigonometrical series, Fundamenta Mathematicae, vol. 26 (1936), pp. 1-43.
  • [1] A. Plessner Über konjugierte trigonometrische Reihen, Comptes Rendus de l'Académie des Sciences de l'URSS, vol. 4 (1935), pp. 251-253.
  • [2] -Über das Verhalten analytischer Funktionen auf dem Rande des Definitionsbereiches, Journal für die reine und angewandte Mathematik, vol. 158 (1928), pp. 219-227.
  • [1] I. Privaloff Sur une généralisation du théorème de Fatou, Récueil Mathématique de Moscou, vol. 31 (1923), pp. 232-235.
  • [1] W. Rogosinki Über die Abschnitte trigonometrischer Reihen, Mathematische Annalen, vol. 95 (1925), pp. 110-134.
  • [1] A. Zygmund Trigonometrical Series, Monografie Matematyczne, vol. 5, Warsaw, 1935.
  • [2] -Einige Sätze aus der Theorie der divergenten Reihen, Bulletin de l'Académie Polonaise, 1928, pp. 309-331.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1941-0005130-1
Article copyright: © Copyright 1941 American Mathematical Society

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