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Israel Journal of Mathematics

, Volume 144, Issue 2, pp 211–219 | Cite as

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

  • E. K. NarayananEmail author
  • S. Thangavelu
Article

Abstract

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.

Keywords

Group Theory Maximal Operator Heisenberg Group Surface Measure Optimal Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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