Skip to main content
Log in

Powers of Sub-Laplacian on Step Two Nilpotent Lie Groups

  • Published:
Journal of Geometric Analysis Aims and scope Submit manuscript

Abstract

We give an explicit, and geometrical formula for the fundamental solution for higher order sub-Laplacians on a model step two nilpotent Lie group.

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.

Similar content being viewed by others

References

  1. Beals, R., Gaveau, B., Greiner, P.: The Green function of model step two hypoelliptic operators and the analysis of certain tangential Cauchy Riemann complexes. Adv. Math. 121, 288–345 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  2. Benson, C., Dooley, A.H., Ratcliff, G.: Fundamental solutions for the powers of the Heisenberg sub-Laplacian. Ill. J. Math. 37, 455–476 (1993)

    MathSciNet  MATH  Google Scholar 

  3. Berenstein, C., Chang, D., Tie, J.: Laguerre Calculus and Its Applications on the Heisenberg Group. American Mathematical Society, International Press, Cambridge (2001). Studies in Advanced Mathematics

    MATH  Google Scholar 

  4. Chang, D.-C., Tie, J.: Estimates for powers of sub-Laplacian on the non-isotropic Heisenberg group. J. Geom. Anal. 10, 653–678 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. Folland, G.B.: A fundamental solution for a subelliptic operator. Bull. Am. Math. Soc. 79(2), 209–223 (1973)

    Article  MathSciNet  Google Scholar 

  6. Hörmander, L.V.: Hypoelliptic second-order differential equations. Acta Math. 119, 147–171 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  7. Nielsen, O.A.: Unitary representations and coadjoint orbits of low-dimensional nilpotent Lie groups. In: Queen’s Papers in Pure and Applied Mathematics, vol. 63. North-Holland, Amsterdam (1983)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ajay Kumar.

Additional information

Communicated by Peter Ebenfelt.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kumar, A., Mishra, M.M. Powers of Sub-Laplacian on Step Two Nilpotent Lie Groups. J Geom Anal 23, 1559–1570 (2013). https://doi.org/10.1007/s12220-012-9298-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12220-012-9298-0

Keywords

Mathematics Subject Classification (2000)

Navigation