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An H1 function with non-summable Fourier expansion

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Harmonic Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 992))

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References

  1. S. Bochner, "Summation of multiple Fourier series by spherical means", Trans. Amer. Math. Soc. 40 (1936), 175–207.

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  2. C.E. Kenig and P.A. Tomas, "Maximal operators defined by Fourier multipliers", Studia Math. 68 (1980), 79–83.

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  3. S.Z. Lu, M. Taibleson, and G. Weiss, "On the almost-everywhere convergence of Bochner-Riesz means of multiple Fourier series", Harmonic Analysis Proceedings, Minneapolis, 1981, Lecture Notes in Math. #908, (1982), 311–318.

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  4. P. Sjölin, "Convergence almost everywhere of certain singular integrals and multiple Fourier series", Arkiv for Mat. 9 (1971), 65–90.

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  5. E.M. Stein, "Localization and summability of multiple Fourier series", Acta Math. 100 (1958), 93–147.

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  6. _____, "On limits of sequences of operators", Ann. of Math., 74 (1961), 140–170.

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  7. E.M. Stein, M. Taibleson, and G. Weiss, "Weak type estimates for maximal operators on certain Hp classes", Rendiconti del Cir. Mat. di Palermo, supplemento, 1981, 81–97.

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  8. E.M. Stein and G. Weiss, "Introduction to Fourier analysis on Eulidean spaces", Princeton University Press, 1971.

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  9. A. Zygmund, "Trigonometric series", 2nd edition, Cambridge University Press, 1959.

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Authors
  1. E. M. Stein
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Giancarlo Mauceri Fulvio Ricci Guido Weiss

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Dedicated to the memory of Salomon Bochner

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© 1983 Springer-Verlag

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Stein, E.M. (1983). An H1 function with non-summable Fourier expansion. In: Mauceri, G., Ricci, F., Weiss, G. (eds) Harmonic Analysis. Lecture Notes in Mathematics, vol 992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069159

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  • DOI: https://doi.org/10.1007/BFb0069159

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12299-9

  • Online ISBN: 978-3-540-39885-1

  • eBook Packages: Springer Book Archive

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