A maximal function on harmonic extensions of $H$-type groups

Vallarino, Maria

Annales mathématiques Blaise Pascal, Tome 13 (2006), p. 87-101 / Harvested from Numdam

Résumé

Let $N$ be an $H$-type group and $S\simeq N\times \mathbb{R}^+$ be its harmonic extension. We study a left invariant Hardy–Littlewood maximal operator $M^{\mathcal{R}}_{\rho }$ 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 $M^{\mathcal{R}}_{\rho }$ is of weak type $(1,1)$.

Détail

Publié le : 2006-01-01

MR 2233012 | Zbl 1137.43003

DOI : https://doi.org/10.5802/ambp.214

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