Israel Journal of Mathematics

, Volume 144, Issue 2, pp 211–219

An optimal theorem for the spherical maximal operator on the Heisenberg group


    • Department of MathematicsIndian Institute of Science
  • S. Thangavelu
    • Stat-Math DivisionIndian Statistical Institute

DOI: 10.1007/BF02916713

Cite this article as:
Narayanan, E.K. & Thangavelu, S. Isr. J. Math. (2004) 144: 211. doi:10.1007/BF02916713


Let\(\mathbb{I}^n = \mathbb{C}^n \times \mathbb{R}\) be the Heisenberg group and μ r be the normalized surface measure on the sphere of radiusr in ℂ n . Let\(Mf = \sup _{r > 0} \left| {f * \mu _r } \right|\). We prove an optimalL p-boundedness result for the spherical maximal functionMf, namely we prove thatM is bounded onL p(I n ) if and only ifp>2n/2n−1.

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© Springer-Verlag 2004