Skip to main content
Log in

Marcinkiewicz multipliers and multi-parameter structure on heisenberg (-type) groups, II

  • 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. Carbery, A., Seeger, A.: Homogeneous Fourier multipliers of Marcinkiewicz type. (preprint)

  2. Christ, M.: The strong maximal function on a nilpotent group. Trans. Amer. Math. Soc.331, 1–13 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  3. Cowling, M., Dooley, A.H., Koranyi, A., Ricci, F.: H-type groups and Iwasawa decompositions. Advances in Math.87, 1–41 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  4. Damek, E., Ricci, F.: Harmonic analysis on solvable extensions of H-type groups. J. Geom. Anal.2, 213–248 (1992)

    MATH  MathSciNet  Google Scholar 

  5. Erdelyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: Higher transcendental functions. Mc Graw-Hill, New York, 1953

    Google Scholar 

  6. Folland, G.B., Stein, E.M.: Hardy spaces on homogeneous groups. Princeton Univ. Press, N.J., 1982

    MATH  Google Scholar 

  7. Gasper, G., Trebels, W.: A characterization of localized Bessel potential spaces and applications to Jacobi and Hankel multipliers. Studia Math.LXV, 243–278 (1979)

    MathSciNet  Google Scholar 

  8. Hebisch, W.: Multiplier theorem on generalized Heisenberg groups. Colloquium Math.LXV, 231–239 (1993)

    MathSciNet  Google Scholar 

  9. Helffer, B., Nourrigat, J.: Caractérisation des opérateurs hypoelliptiques homogènes invariants à gauche sur un groupe de Lie nilpotent gradué. Comm. in Partial Diff. Eq.4, 899–958 (1979)

    MATH  MathSciNet  Google Scholar 

  10. Hulanicki, A.: A functional calculus for Rockland operators on nilpotent Lie groups. Studia Math.78, 253–266 (1984)

    MATH  MathSciNet  Google Scholar 

  11. Kaplan, A.: Fundamental solutions for a class of hypoelliptic p.d.e. generated by composition of quadratic forms. Trans. Amer. Math. Soc.258, 147–153 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  12. Mauceri, G.: Maximal operators and Riesz means on stratified groups. Symposia Math.XXIX, 46–62

  13. Metivier, G.: Hypoelliticité analytique sur des groupes nilpotents de rang 2. Duke Math. J.47, 195–221 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  14. Müller, D., Ricci, F.: Solvability for a class of doubly characteristic differential operators on 2-step nilpotent groups. (to appear in Annals of Math)

  15. Müller D., Ricci, F., Stein, E.M.: Marcinkiewicz multipliers and two-parameter structures on Heisenberg groups I. Invent. Math.119, 119–233 (1995)

    Article  Google Scholar 

  16. Müller, D., Stein, E.M.: On spectral multipliers for Heisenberg and related groups. J. Math. Pures Appl.73, 413–440 (1994)

    MATH  MathSciNet  Google Scholar 

  17. Ricci, F.: Harmonic analysis on generalized Heisenberg groups. (unpublished preprint)

  18. Ricci, F., Sjögren, P.: Two-parameter maximal functions in the Heisenberg group. Math. Zeitschrift199, 565–575 (1988)

    Article  MATH  Google Scholar 

  19. Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton Univ. Press, N.J., 1970

    MATH  Google Scholar 

  20. Stein, E.M., Weiss, G.: Introduction to Fourier analysis on Euclidean spaces. Princeton Univ. Press, 1971

  21. Strichartz, R.S.:L p harmonic analysis and Radon transforms on the Heisenberg group. J. Funct. Anal.96, 350–406 (1991)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Müller, D., Ricci, F. & Stein, E.M. Marcinkiewicz multipliers and multi-parameter structure on heisenberg (-type) groups, II. Math Z 221, 267–291 (1996). https://doi.org/10.1007/BF02622116

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02622116

Keywords

Navigation