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A weak-type estimate for Fourier-Bessel multipliers

Authors: John Gosselin and Krzysztof Stempak
Journal: Proc. Amer. Math. Soc. 106 (1989), 655-662
MSC: Primary 42B15
MathSciNet review: 1004428
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Abstract: We apply Hörmander's technique to prove a weak-type $ (1,1)$ estimate for multiplier operators with respect to the Fourier-Bessel transform. This improves a result in [4, 5].

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  • [2] R. E. Edwards and G. I. Gaudry, Littlewood-Paley and multiplier theory, Springer-Verlag, Berlin-New York, 1977. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 90. MR 0618663
  • [3] Lars Hörmander, Estimates for translation invariant operators in 𝐿^{𝑝} spaces, Acta Math. 104 (1960), 93–140. MR 0121655
  • [4] Krzysztof Stempak, La théorie de Littlewood-Paley pour la transformation de Fourier-Bessel, C. R. Acad. Sci. Paris Sér. I Math. 303 (1986), no. 1, 15–18 (French, with English summary). MR 849618
  • [5] -, The Littlewood-Paley theory for the Fourier-Bessel transform, Univ.of Wroclaw, Preprint no. 45, 1985.

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Keywords: Fourier-Bessel transform, multipliers, generalized convolution
Article copyright: © Copyright 1989 American Mathematical Society