Mathematische Annalen

, Volume 267, Issue 1, pp 1–15

Estimates for singular convolution operators on the Heisenberg group

  • D. Geller
  • E. M. Stein
Article

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References

  1. 1.
    Geller, D.: Spherical harmonics, the Weyl transform and the Fourier transform on the Heisenberg group. PreprintGoogle Scholar
  2. 2.
    Geller, D., Stein, E.M.: Singular convolution operators on the Heisenberg group. Bull. Am. Math. Soc.6, 99–103 (1982)Google Scholar
  3. 3.
    Grossman, A., Loupias, G., Stein, E.M.: An algebra of pseudo-differential operators and quantum mechanics in phase space. Ann. Inst. Fourier (Grenoble)18, 343–368 (1969)Google Scholar
  4. 4.
    Howe, R.: Quantum mechanics and partial differential equations. J. Func. Anal.38, 188–254 (1980).Google Scholar
  5. 5.
    Koranyi, A., Vagi, S.: Singular integrals on homogeneous spaces and some problems of classical analysis. Ann. Scoula Norm. Sup. Pisa25, 575–648 (1971)Google Scholar
  6. 6.
    Mauceri, G., Picardello, M.A., Ricci, F.: Twisted convolution, Hardy spaces and Hörmander multipliers. Supp. Rend. Circ. Mat. Palermo1, 191–202 (1981)Google Scholar
  7. 7.
    Müller, D.: Calderón-Zygmund kernels carried by linear subspaces of homogeneous nilpotent Lie algebras. Invent. Math.73, 467–489 (1983)Google Scholar
  8. 8.
    Nagel, A., Stein, E.M.: Lectures on pseudo-differential operators: regularity theorems and applications to non-elliptic problems. Princeton, NJ: Princeton University Press 1979Google Scholar
  9. 9.
    Phong, D.H., Stein, E.M.: Singular integrals with kernels of mixed homogeneity. Conference on Harmonic Analysis in Honor of Antoni Zygmund. Eds. Beckner, W., Calderón, A., Fefferman, R., Jones, P., Wadsworth International Group 327-339 (1982)Google Scholar
  10. 10.
    Ricci, F.: Calderón-Zygmund kernels on nilpotent Lie groups. In: Lecture Notes in Mathematics, Vol. 908, pp. 217–227. Berlin, Heidelberg, New York: Springer 1982Google Scholar
  11. 11.
    Segal, I.: Transforms for operators and symplectic automorphisms over a locally compact abelian group. Math. Scand.13, 31–43 (1963)Google Scholar
  12. 12.
    Stein, E.M., Weiss, G.: Introduction to Fourier analysis on Euclidean spaces. Princeton, NJ: Princeton University Press 1971Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • D. Geller
    • 1
    • 2
  • E. M. Stein
    • 1
    • 2
  1. 1.Department of MathematicsSUNY at Stony BrookStony BrookUSA
  2. 2.Department of MathematicsPrinceton UniversityPrincetonUSA

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