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Consider the maximal function defined by $Mf=\\sup_{t>0} |f*\\mu_t|$. We prove for $n\\ge 2$ that $M$ defines an operator bounded on $L^p(H^n)$ provided that $p>2n/(2n-1)$. This improves an earlier result by Nevo and Thangavelu, and the range for $L^p$ boundedness is optimal. 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