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A weighted uniform $L^{p}$-estimate of Bessel functions: A note on a paper of Guo

Author(s): Krzysztof Stempak
Journal: Proc. Amer. Math. Soc. 128 (2000), 2943-2945.
MSC (1991): Primary 33C10
Posted: March 2, 2000
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Abstract: An improved Guo's uniform $L^{p}$ estimate of Bessel functions is shown by using a uniform pointwise bound of Barceló and Córdoba.

References:

[BC]
J. A. Barceló, A. Córdoba, Band-limited functions: $L^{p}$-convergence, Trans. Amer. Math. Soc. 313 (1989), 655-669. MR 90g:42017

[C]
A. Córdoba, The disc multiplier, Duke Math. J. 58 (1989), 21-29. MR 90j:42038

[Guo]
K. Guo, A uniform $L^{p}$ estimate of Bessel functions and distributions supported on $S^{n-1}$, Proc. Amer. Math. Soc. 125 (1997), 1329-1340. MR 97g:46047

[Va]
J. L. Varona, Fourier series of functions whose Hankel transform is supported on [0,1], Constr. Approx. 10 (1994), 65-75. MR 94m:42071

[W]
G. N. Watson, A treatise on the theory of Bessel functions, Cambridge University Press, Cambridge, 1966.

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Additional Information:

Krzysztof Stempak
Affiliation: Instytut Matematyki Politechniki Wroclawskiej, ul.Wyb. Wyspianskiego 27, 50-370 Wroclaw, Poland
Email: stempak@ulam.im.pwr.wroc.pl

DOI: 10.1090/S0002-9939-00-05365-X
PII: S 0002-9939(00)05365-X
Keywords: Bessel functions, uniform estimates
Received by editor(s): August 1, 1998
Received by editor(s) in revised form: November 11, 1998
Posted: March 2, 2000
Additional Notes: This research was supported in part by KBN grant # 2 PO3A 048 15 and European Commision via the TMR network ``Harmonic analysis'', contract no: ERB FMRX--CT97--0159.
Communicated by: Christopher D. Sogge
Copyright of article: Copyright 2000, American Mathematical Society

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