Israel Journal of Mathematics

, Volume 141, Issue 1, pp 315–340 | Cite as

Singular spherical maximal operators on a class of two step nilpotent lie groups

  • Detlef Müller
  • Andreas Seeger


LetH n ≅ℝ2n ⋉ℝ be the Heisenberg group and letμ t be the normalized surface measure for the sphere of radiust in ℝ2n . Consider the maximal function defined byM f=supt>0|f*μ t |. We prove forn≥2 thatM defines an operator bounded onL p (H n ) provided thatp>2n/(2n−1). This improves an earlier result by Nevo and Thangavelu, and the range forL p boundedness is optimal. We also extend the result to a more general class of surfaces and to groups satisfying a nondegeneracy condition; these include the groups of Heisenberg type.


Heisenberg Group Fourier Integral Operator Nondegeneracy Condition Schwartz Kernel Heisenberg Type 
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© Hebrew University 2004

Authors and Affiliations

  1. 1.Mathematisches SeminarChristian-Albrechts-Universität zu KielKielGermany
  2. 2.Department of MathematicsUniversity of WisconsinMadisonUSA

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