A uniform $L^p$ estimate of Bessel functions and distributions supported on $S^{n-1}$
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Abstract:
A uniform $L^p$ estimate of Bessel functions is obtained, which is used to get a characterization of the $L^2$ measures on the unit sphere of $R^n$ in terms of the mixed $L^p$ norm of the Fourier transform of the measures.References
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Additional Information
- Kanghui Guo
- Affiliation: Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804
- Email: kag026f@cnas.smsu.edu
- Received by editor(s): March 14, 1995
- Received by editor(s) in revised form: October 11, 1995
- Additional Notes: The author’s research was supported in part by the National Science Foundation, Grant DMS-9401208. Some of the work was done while the author was attending the harmonic analysis workshop at Edinburgh, Scotland, June, 1994.
- Communicated by: Christopher D. Sogge
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1329-1340
- MSC (1991): Primary 43A45
- DOI: https://doi.org/10.1090/S0002-9939-97-03667-8
- MathSciNet review: 1363462