Fourier series and mean moduli of continuity
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- Trans. Amer. Math. Soc. 42 (1937), 366-395 Request permission
References
-
S. Bernstein. Sur la convergence absolue des séries trigonométriques. Comptes Rendus des Séances de l’Académie des Sciences, Paris, vol. 158 (1914), pp. 1661-1663.
—. Same title. Communications de la Société Mathématique de Kharkoff, vol. 14 (1914), pp. 139-144 (in Russian).
—. Same title. Comptes Rendus, vol. 199 (1934), pp. 397-400.
- G. H. Hardy and J. E. Littlewood, Some properties of fractional integrals. I, Math. Z. 27 (1928), no. 1, 565–606. MR 1544927, DOI 10.1007/BF01171116
- G. H. Hardy and J. E. Littlewood, A convergence criterion for Fourier series, Math. Z. 28 (1928), no. 1, 612–634. MR 1544980, DOI 10.1007/BF01181186 —. Notes on the theory of series. IX. On the absolute convergence of Fourier series. Journal of the London Mathematical Society, vol. 3 (1928), pp. 250-253. G. H. Hardy, J. E. Littlewood, and G. Pólya. Inequalities. Cambridge, 1934.
- Einar Hille and J. D. Tamarkin, On the summability of fourier series. III, Math. Ann. 108 (1933), no. 1, 525–577. MR 1512863, DOI 10.1007/BF01452851 K. Nabetani. Remarks on some theorems concerning sections of a power series. Tôhoku Mathematical Journal, vol. 41 (1935-36), pp. 333-336.
- Freidrich Riesz, Über die Randwerte einer analytischen Funktion, Math. Z. 18 (1923), no. 1, 87–95 (German). MR 1544621, DOI 10.1007/BF01192397 M. Riesz. Eine trigonometrische Interpolationsformel und einige Ungleichungen fur Polynome. Jahresbericht der Deutschen Mathematiker-Vereinigung, vol. 23 (1914), pp. 354-368. O. Szász. Über den Konvergenzexponenten der Fourierschen Reihen gewisser Funktionenklassen. Sitzungsberichte der Bayerischen Akademie der Wissenschaften, München, 1922, pp. 135-150. —. Korlátos hatványsorokról, Matematikai és Természettudomanyi Ertesitö, vol. 43 (1926), pp. 504-520.
- Otto Szász, Über die Fourierschen Reihen gewisser Funktionenklassen, Math. Ann. 100 (1928), no. 1, 530–536 (German). MR 1512500, DOI 10.1007/BF01448861 E. C. Titchmarsh. A note on Fourier transforms. Journal of the London Mathematical Society, vol. 2 (1927), pp. 148-150. Z. Waraszkiewicz. Sur un théorème de M. Zygmund. Bulletin International de l’Académie Polonaise, Classe A, Cracovie, 1929, pp. 275-279. A. Zygmund. A remark on conjugate series. Proceedings of the London Mathematical Society, (2), vol. 34 (1932), pp. 392-400.
- Antoni Zygmund, Some points in the theory of trigonometric and power series, Trans. Amer. Math. Soc. 36 (1934), no. 3, 586–617. MR 1501757, DOI 10.1090/S0002-9947-1934-1501757-2 —. Trigonometrical Series. Warsaw-Lwów, 1935.
Additional Information
- © Copyright 1937 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 42 (1937), 366-395
- MSC: Primary 42A16
- DOI: https://doi.org/10.1090/S0002-9947-1937-1501927-6
- MathSciNet review: 1501927