Singular spherical maximal operators on a class of two step nilpotent lie groups |
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Authors: | Email author" target="_blank">Detlef?MüllerEmail author Andreas?Seeger |
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Institution: | 1.Mathematisches Seminar,Christian-Albrechts-Universit?t zu Kiel,Kiel,Germany;2.Department of Mathematics,University of Wisconsin,Madison,USA |
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Abstract: | 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=sup
t>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.
The second author was supported in part by the National Science Foundation. |
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Keywords: | |
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