Fonctions maximales centrées de Hardy–Littlewood sur les groupes de Heisenberg
Tom 191 / 2009
Studia Mathematica 191 (2009), 89-100
MSC: 42B25, 43A80.
DOI: 10.4064/sm191-1-7
Streszczenie
By getting uniformly asymptotic estimates for the Poisson kernel on Heisenberg groups $\mathbb{H}_{2 n +1}$, we prove that there exists a constant $A > 0$, independent of $n \in {\mathbb N}^*$, such that for all $f \in L^1(\mathbb{H}_{2n +1})$, we have $\| M f \|_{L^{1, \infty}} \leq A n \| f \|_1$, where $M$ denotes the centered Hardy–Littlewood maximal function defined by the Carnot–Carathéodory distance or by the Korányi norm.
