Skip to main content
Log in

L p -L p-Estimates for Fourier integral operators related to hyperbolic equations

  • Published:
Mathematische Zeitschrift 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. Brenner, P.: OnL p -L p-estimates for the wave-equation. Math. Z.145, 251–254 (1975)

    Google Scholar 

  2. Chazarain, J.: Opérateurs hyperboliques à caractéristiques de multiplicité constante. Ann. Inst. Fourier24, 173–202 (1974)

    Google Scholar 

  3. Duistermaat, H.: Fourier Integral Operators. Lecture notes, Courant Institute of Mathematical Sciences, New York, 1973

    Google Scholar 

  4. Hörmander, L.: The spectral functionof an elliptic operator, Acta math.121, 193–218 (1968)

    Google Scholar 

  5. Hörmander, L.: Pseudo-differential operators and hypo-elliptic equations. In: Singular Integrals (Chicago 1966). Proceedings of Symposia in Pure Mathematics10, pp. 138–183. Providence: American Mathematical Society 1967

    Google Scholar 

  6. Hörmander, L.: Fourier Integral Operators I. Acta math.127, 79–183, (1971)

    Google Scholar 

  7. Littman, W.: Fourier transforms of surface carried measures and differentiation of surface averages. Bull. Amer. math. Soc.69, 766–770, (1963)

    Google Scholar 

  8. Littman, W.:L p-L q-estimates for singular integral operators arising from hyperbolic equations, In: Partial Differential Equations. (Berkeley 1971). Proceedings of Symposia in Pure Mathematics23. pp. 479–481 Providence: American Mathematical Society 1973

    Google Scholar 

  9. Littman, W., McCarthy, C., Riviere, N.: The non-existence ofL p estimates for certain translation invariant operators. Studia math.30, 219–229 (1968)

    Google Scholar 

  10. Löfström, J.: Besov spaces in the theory of approximation. Ann. Mat. pura appl., IV Ser.85, 93–184 (1970)

    Google Scholar 

  11. Löfström, J., Thomée, V.: Convergence analysis of finite difference schemes for semi-linear initial value problems. Revue Franç. Automat. Inform. Rech. opérat. (To appear)

  12. Peetre, J.: Applications de la théorie des espace d'interpolation dans l'analyse harmonique. Richereche Mat.15, 1–36 (1966)

    Google Scholar 

  13. Strichartz, R.S.: Convolutions with kernels having singularities on a sphere. Trans. Amer. math. Soc.148, 461–471 (1970)

    Google Scholar 

  14. Strichartz, R.S.: A priori estimates for the wave equation and some applications. J. functional Analysis5, 218–235 (1970)

    Google Scholar 

  15. Taiblesson, M.H.: On the theory of Lipschitz-spaces of distributions on Euclideann-space I. J. Math. Mech.13, 407–479 (1964)

    Google Scholar 

  16. Triebels, H.: Spaces of distributions of Besov spaces on Euclideann-space. Duality, interpolation. Ark. Mat.11, 13–64 (1973)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brenner, P. L p -L p-Estimates for Fourier integral operators related to hyperbolic equations. Math Z 152, 273–286 (1977). https://doi.org/10.1007/BF01488969

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01488969

Keywords

Navigation