Keywords
- Fourier Series
- Inverse Fourier Transform
- Critical Index
- Fourier Multiplier
- mUltiplier Operator
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References
S. Bochner, "Summation of multiple Fourier series by spherical means", Trans. Amer. Math. Soc. 40 (1936), 175–207.
C.E. Kenig and P.A. Tomas, "Maximal operators defined by Fourier multipliers", Studia Math. 68 (1980), 79–83.
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.
P. Sjölin, "Convergence almost everywhere of certain singular integrals and multiple Fourier series", Arkiv for Mat. 9 (1971), 65–90.
E.M. Stein, "Localization and summability of multiple Fourier series", Acta Math. 100 (1958), 93–147.
_____, "On limits of sequences of operators", Ann. of Math., 74 (1961), 140–170.
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.
E.M. Stein and G. Weiss, "Introduction to Fourier analysis on Eulidean spaces", Princeton University Press, 1971.
A. Zygmund, "Trigonometric series", 2nd edition, Cambridge University Press, 1959.
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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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