Skip to main content
Log in

Oscillatory integrals and atoms on the unit sphere

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Colzani, L.,Hardy spaces on spheres, Ph.D. Thesis, Washington University, St. Louis, 1982

    Google Scholar 

  2. Colzani, L.,Lipschitz spaces on compact rank one symmetric spaces, Harmonic analysis (Cortona, 1982) 139–160, Lecture Notes in Math.992, Springer, Berlin-New York, 1983

    Google Scholar 

  3. Cowling, M., Disney, S., Mauceri, G. and Müller, D.,Damping oscillatory integrals, Invent. Math.101 (1990), 237–260

    Article  MATH  MathSciNet  Google Scholar 

  4. Duoandikoetxea, J. and Rubio de Francia, J.L.,Maximal and singular integral operators via Fourier transform estimates, Invent. Math.84 (1986), 541–561

    Article  MATH  MathSciNet  Google Scholar 

  5. Fan, D.,Restriction theorems related to atoms, IIl. Jour. Math., to appear

  6. Herz, C.,Fourier transforms related to convex sets, Ann. of Math.75 (1962), 81–92

    Article  MathSciNet  Google Scholar 

  7. Hlawka, E., Über Integrale auf Konvexen Körper I, Monatsh Math.54 (1950), 1–36

    Article  MathSciNet  Google Scholar 

  8. Littman, W.,Fourier transforms of surface-carried measures and differentiability of surface averages, Bull. Amer. Math. Soc.69 (1963), 766–770

    Article  MATH  MathSciNet  Google Scholar 

  9. Randol, B.,On the Fourier transform of the indicator function of a planar set, Trans. Amer. Math. Soc.139 (1969), 271–278

    Article  MATH  MathSciNet  Google Scholar 

  10. Randol, B.,On the asymptotic behavior of the Fourier transform of the indicator function of a convex set, Trans. Amer. Math. Soc.139 (1969), 279–285

    Article  MATH  MathSciNet  Google Scholar 

  11. Ricci, F. and Stein, E.M.,Harmonic analysis on nilpotent groups and singular integrals I: Oscillatory integrals, Jour. Func. Anal.73 (1987), 179–194

    Article  MATH  MathSciNet  Google Scholar 

  12. Sogge, C. and Stein, E.M.,Averages of functions over hypersurfaces in R n, Invent. Math.82 (1985), 543–556

    Article  MATH  MathSciNet  Google Scholar 

  13. Stein, E.M., “Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals,” Princeton University Press, Princeton, NJ, 1993

    MATH  Google Scholar 

  14. Svensson, I.,Estimates for the Fourier transform of the characteristic function of a convex set, Ark. Mat.9 (1971), 11–22

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported in part by a grant from the National Science Foundation

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fan, D., Pan, Y. Oscillatory integrals and atoms on the unit sphere. Manuscripta Math 89, 179–192 (1996). https://doi.org/10.1007/BF02567512

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02567512

Keywords

Navigation