Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



A uniform $L^p$ estimate of Bessel functions
and distributions supported on $S^{n-1}$

Author: Kanghui Guo
Journal: Proc. Amer. Math. Soc. 125 (1997), 1329-1340
MSC (1991): Primary 43A45
MathSciNet review: 1363462
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. S. Agmon and L. Hörmander, Asymptotic properties of solutions of differential equations with simple characteristics, Journal D'Analyse Mathematique 30 (1976), 1-38. MR 57:6776
  • 2. K. Guo, On the $p$-approximation property for hypersurfaces of $R^n$, Math. Proc. Camb. Phil. Soc. 105 (1989), 503-511. MR 90f:42013
  • 3. L. Hörmander, Lower bounds at infinity for solutions of differential equations with constant coefficients, Israel J. Math. 16 (1973), 103-116. MR 49:5543
  • 4. L. Hörmander, The analysis of linear partial differential operators I, Springer-Verlag, 1990.
  • 5. R. A. Hunt, On the $L(p,q)$ spaces, Enseign. Math. 12 (1966), 248-275. MR 36:6921
  • 6. C. E. Kenig, A. Ruiz, and C. D. Sogge, Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators, Duke Mathematical Journal 55 (1987), 329-347. MR 88d:35037
  • 7. W. Littman, Fourier transforms of surface-carried measures and differentiability of surface average, Bull. Amer. Math. Soc. 69 (1963), 766-770. MR 27:5086
  • 8. L. Schwartz, Sur une propriete de synthese spectrale dans les groupes non compact, C. R. Acad. Sci. Paris. 227 (1948), 424-426. MR 10:249e
  • 9. C. D. Sogge, Fourier integrals in classical analysis, Cambridge University Press, 1993. MR 94e:35178
  • 10. E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, 1971. MR 46:4102
  • 11. E. M. Stein, Harmonic Analysis, Princeton University Press, 1993. MR 95c:42002
  • 12. L. Vega, Restriction theorems and the Schrödinger multiplier on the torus, Partial differential equations with minimal smoothness and applications (B. Dahlberg et al., eds.), IMA Vol. Math. Appl., vol. 42, Springer-Verlag, New York, 1992, 199-211. MR 93e:42025
  • 13. G. N. Watson, A treatise on the theory of Bessel functions, Cambridge University Press, 1958. MR 6:64a

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 43A45

Retrieve articles in all journals with MSC (1991): 43A45

Additional Information

Kanghui Guo
Affiliation: Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804

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
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society