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Transactions of the American Mathematical Society

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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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    A. F. Andersen Studier over Cesàro’s Summabilitetsmetode, Copenhagen, Gjellerup, 1921. 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. G. H. Hardy and M. Riesz Dirichlet’s Series, Cambridge Tracts, Cambridge, 1915.
  • J. Karamata, Über die Hardy-Littlewoodschen Umkehrungen des Abelschen Stetigkeitssatzes, Math. Z. 32 (1930), no. 1, 319–320 (German). MR 1545168, DOI https://doi.org/10.1007/BF01194636
  • E. Kogbetliantz Sommation des séries et intégrales divergentes, Mémorial des Sciences Mathématiques, vol. 51, pp. 1-75. B. Kuttner A theorem on trigonometric series, Journal of the London Mathematical Society, vol. 10 (1935), pp. 131-140.
  • J. Marcinkiewicz, Sur la sommabilité forte de séries de Fourier, J. London Math. Soc. 14 (1939), 162–168 (French). MR 66, DOI https://doi.org/10.1112/jlms/s1-14.3.162
  • J. Marcinkiewicz and A. Zygmund On the differentiability of functions and summability of trigonometrical series, Fundamenta Mathematicae, vol. 26 (1936), pp. 1-43. A. Plessner Über konjugierte trigonometrische Reihen, Comptes Rendus de l’Académie des Sciences de l’URSS, vol. 4 (1935), pp. 251-253. ---Über das Verhalten analytischer Funktionen auf dem Rande des Definitionsbereiches, Journal für die reine und angewandte Mathematik, vol. 158 (1928), pp. 219-227. I. Privaloff Sur une généralisation du théorème de Fatou, Récueil Mathématique de Moscou, vol. 31 (1923), pp. 232-235. W. Rogosinki Über die Abschnitte trigonometrischer Reihen, Mathematische Annalen, vol. 95 (1925), pp. 110-134. A. Zygmund Trigonometrical Series, Monografie Matematyczne, vol. 5, Warsaw, 1935. ---Einige Sätze aus der Theorie der divergenten Reihen, Bulletin de l’Académie Polonaise, 1928, pp. 309-331.

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Article copyright: © Copyright 1941 American Mathematical Society