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Bulletin of the American Mathematical Society

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The strong summability of double Fourier series


Author: Hai-Tsin Hsü
Journal: Bull. Amer. Math. Soc. 51 (1945), 700-713
DOI: https://doi.org/10.1090/S0002-9904-1945-08422-5
MathSciNet review: 0012692
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References | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. G. H. Hardy and J. E. Littlewood, Sur la series de Fourier d'une fonction à carré sommable, C. R. Acad. Sci. Paris vol. 156 (1913) pp. 1307-1309.
  • 2. G. H. Hardy and J. E. Littlewood, Notes on the theory of series (IV): On the strong summability of Fourier series, Proc. London Math. Soc. (2) vol. 26 (1927) pp. 273-286.
  • 3. G. H. Hardy and J. E. Littlewood, The strong summability of Fourier series, Fund. Math. vol. 25 (1935) pp. 162-189.
  • 4. G. H. Hardy and J. E. Littlewood, A maximal theorem with function-theoretic applications, Acta Math. 54 (1930), no. 1, 81–116. MR 1555303, https://doi.org/10.1007/BF02547518
  • 5. B. Jessen, J. Marcinkiewicz and A. Zygmund, Note on the differentiability of multiple integrals, Fund. Math. vol. 25 (1935) pp. 217-234.
  • 6. J. Marcinkiewicz, Sur la sommabilité forte de séries de Fourier, J. London Math. Soc. vol. 14 (1939) pp. 162-168. MR 66
  • 7. M. Riesz, Sur les maxima des formes billinéaires et sur les fonctionnelles linéaires, Acta Math. vol. 49 (1926) pp. 465-497.
  • 8. S. Saks, Remark on the differentiability of the Lebesgue indefinite integral, Fund. Math. vol. 22 (1934) pp. 257-261.
  • 9. S. Saks, Theory of integrals, Monografje Matematyczne, Warsaw, 1937.
  • 10. W. H. Young, Multiple Fourier series, Proc. London Math. Soc, (2) vol. 11 (1913) pp. 133-184.
  • 11. A. Zygmund, On the differentiability of multiple integrals, Fund. Math. vol. 23 (1934) pp. 143-149.
  • 12. A. Zygmund, On the convergence and summability of power series on the circle of convergence (II), Proc. London Math. Soc. vol. 47 (1942) pp. 326-350. MR 7042
  • 13. A. Zygmund, Trigonometrical series, Monografje Matematyczne, Warsaw, 1935.


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1945-08422-5

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