Singular Spherical Maximal Operators on a Class of Two Step Nilpotent Lie Groups

نویسندگان

  • Detlef Müller
  • Andreas Seeger
  • DETLEF MÜLLER
  • ANDREAS SEEGER
چکیده

Let H be the Heisenberg group and let μt be the normalized surface measure for the sphere of radius t in R. Consider the maximal function defined by Mf = supt>0 |f ∗μt|. We prove for n ≥ 2 that M defines an operator bounded on L(H) provided that p > 2n/(2n − 1). This improves an earlier result by Nevo and Thangavelu, and the range for L boundedness is optimal. We also extend the result to a more general setting of surfaces and to groups satisfying a nondegeneracy condition; these include the groups of Heisenberg type.

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Singular Spherical Maximal Operators on a Class of Step Two Nilpotent Lie Groups

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تاریخ انتشار 2003