Let $N$ be an $H$-type group and $Ssimeq Nimes mathbb{R}^+$ be its harmonic extension. We study a left invariant Hardy–Littlewood maximal operator $M^{mathcal{R}}_{ho }$ on $S$, obtained by taking maximal averages with respect to the right Haar measure over left-translates of a family $mathcal{R}$ of neighbourhoods of the identity. We prove that the maximal operator $M^{mathcal{R}}_{ho }$ is of weak type $(1,1)$.
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机译：假设$ N $是$ H $类型的组，而$ S simeq N times mathbb {R} ^ + $是其谐波扩展。我们研究了$ S $上的左不变Hardy–Littlewood最大算子$ M ^ { mathcal {R}} _ { rho} $，该值是通过对一个家庭的左平移取相对于右Haar测度的最大平均值而获得的$ mathcal {R} $身份的邻居。我们证明最大运算符$ M ^ { mathcal {R}} _ { rho} $是弱类型$（1,1）$。
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