Israel Journal of Mathematics

, Volume 144, Issue 2, pp 211–219

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



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


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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.Stat-Math DivisionIndian Statistical InstituteBangaloreIndia

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