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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A weak-type estimate for Fourier-Bessel multipliers
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by John Gosselin and Krzysztof Stempak PDF
Proc. Amer. Math. Soc. 106 (1989), 655-662 Request permission

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].
References
  • Ronald R. Coifman and Guido Weiss, Analyse harmonique non-commutative sur certains espaces homogènes, Lecture Notes in Mathematics, Vol. 242, Springer-Verlag, Berlin-New York, 1971 (French). Étude de certaines intégrales singulières. MR 0499948
  • R. E. Edwards and G. I. Gaudry, Littlewood-Paley and multiplier theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 90, Springer-Verlag, Berlin-New York, 1977. MR 0618663
  • Lars Hörmander, Estimates for translation invariant operators in $L^{p}$ spaces, Acta Math. 104 (1960), 93–140. MR 121655, DOI 10.1007/BF02547187
  • 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
  • —, The Littlewood-Paley theory for the Fourier-Bessel transform, Univ.of Wroclaw, Preprint no. 45, 1985.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 106 (1989), 655-662
  • MSC: Primary 42B15
  • DOI: https://doi.org/10.1090/S0002-9939-1989-1004428-6
  • MathSciNet review: 1004428