Riesz means for the sublaplacian on the Heisenberg group

  • S Thangavelu


The uniform boundedness of the Riesz means for the sublaplacian on the Heisenberg groupH n is considered. It is proved thatS R α are uniformly bounded onL p(Hn) for 1≤p≤2 provided α>α(p)=(2n+1)[(1/p)−(1/2)].


Fourier transform representations sublaplacian Riesz means projections 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Fefferman C, A note on spherical summation multipliers,Israel J. Math. 15 (1973) 44–58MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Geller D, Fourier Analysis on the Heisenberg group,J. Funct. Anal. 36 (1980) 205–254MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Kunze R A,L p Fourier transforms on locally compact unimodular groups,Trans. Am. Math. Soc. 89 (1958) 519–540CrossRefMathSciNetGoogle Scholar
  4. [4]
    Markett C, Mean Cesaro summability of Laguerre expansions and norm estimates with shifted parameter,Anal. Math. 8 (1982) 19–37MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Mauceri G, Riesz means for the eigenfunction expansions for a class of hypoelliptic differential operators,Ann. Inst. Fourier Grenoble 31 (1981) 115–140MATHMathSciNetGoogle Scholar
  6. [6]
    Sogge C D, On the convergence of Riesz means on compact manifolds,Ann. Math. 126 (1987) 439–447CrossRefMathSciNetGoogle Scholar
  7. [7]
    Szego G, Orthogonal polynomials,Am. Math. Soc. Colloq. Public, providence, R.I. (1967)Google Scholar
  8. [8]
    Thangavelu S, Hermite expansions on\(\mathbb{R}^{2n} \) for radial functions,Revist. Math. Ibero. (to appear)Google Scholar
  9. [9]
    Thangavelu S, Weyl multipliers, Bochner-Riesz means and special Hermite expansions, Preprint (1989)Google Scholar

Copyright information

© Indian Academy of Sciences 1990

Authors and Affiliations

  • S Thangavelu
    • 1
  1. 1.TIFR CentreBangaloreIndia

Personalised recommendations