Skip to main content
SpringerLink
Log in

Sharp inequalities for Weyl operators and Heisenberg groups

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Babenko, K.I.: An inequality in the theory of Fourier integrals. Izv. Akad. Nauk SSSR, Ser. Mat.25, 531–542 (1961). English translation, Amer. Math. Soc. Transl.44, 115–128 (1965)

    Google Scholar 

  2. Beckner, W.: Inequalities in Fourier analysis. Ann. of Math.102, 159–182 (1975)

    Google Scholar 

  3. Brascamp, H.J., Lieb, E.H.: Best constants in Young's inequality, its converse, and its generalization to more than three functions. Adv. in Math.20, 151–173 (1976)

    Google Scholar 

  4. Fournier, J.J.F.: Sharpness in Young's inequality for convolution. Pac. J. Math.72, 383–397 (1977)

    Google Scholar 

  5. Hewitt, E., Ross, K.A.: Abstract harmonic analysis. Berlin, Heidelberg, New York: Springer, I: 1963, II: 1970

    Google Scholar 

  6. Hewitt, E., Stromberg, K.: Real and abstract analysis. Berlin, Heidelberg, New York: Springer 1969

    Google Scholar 

  7. Khalil, I.: Sur l'analyse harmonique du groupe affine de la droite. Stud. Math.51, 139–167 (1974)

    Google Scholar 

  8. Kleppner, A., Lipsman, R.L.: The Plancherel formula for group extensions. I. Ann. Sci. Ec. Norm. Sup.5, 459–516 (1972); II.6, 103–132 (1973)

    Google Scholar 

  9. Kunze, R.A.:L p-Fourier transforms on locally compact unimodular groups. Trans. Amer. Math. Soc.89, 519–540 (1958)

    Google Scholar 

  10. Lipsman, R.L.: Non-abelian Fourier analysis. Bull. Sci. Math.98, 109–233 (1974)

    Google Scholar 

  11. Reed, M., Simon, B.: Methods of modern mathematical physics. II: Fourier analysis, self-adjointness. New York, London: Academic Press 1975

    Google Scholar 

  12. Russo, B.: The norm of theL p-Fourier transform on unimodular groups. Trans. Amer. Math. Soc.192, 293–305 (1974)

    Google Scholar 

  13. Russo, B.: The norm of theL p-Fourier transform. II. Can. J. Math.28, 1121–1131 (1976)

    Google Scholar 

  14. Russo, B.: On the Hausdorff Young theorem for integral operators. Pac. J. Math.68, 241–253 (1977)

    Google Scholar 

  15. Wolf, J.: Representations of certain semi-direct product groups. J. Funct. Anal.19, 339–372 (1975)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, 92717, Irvine, CA, USA

    Abel Klein & Bernard Russo

Authors
  1. Abel Klein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bernard Russo
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Partially supported by the N.S.F. under grant MCS-76 06332

Partially supported by the N.S.F. under grant MCS-76 07219

Rights and permissions

Reprints and permissions

About this article

Cite this article

Klein, A., Russo, B. Sharp inequalities for Weyl operators and Heisenberg groups. Math. Ann. 235, 175–194 (1978). https://doi.org/10.1007/BF01405012

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01405012

Keywords

Search

Navigation