Erratum : “On the supercuspidal representations of the product of two primes”
We obtain an estimate for the Poisson kernel for the class of second order left-invariant differential operators on higher rank NA groups.
This is a short description of some results obtained by Ewa Damek, Andrzej Hulanicki, Richard Penney and Jacek Zienkiewicz. They belong to harmonic analysis on a class of solvable Lie groups called NA. We apply our results to analysis on classical Siegel domains.
For rank one solvable Lie groups of the type NA estimates for the Poisson kernels and their derivatives are obtained. The results give estimates on the Poisson kernel and its derivatives in a natural parametrization of the Poisson boundary (minus one point) of a general homogeneous, simply connected manifold of negative curvature.
On montre que la fonction maximale de Hardy-Littlewood est de type sur certains groupes de Lie et variétés de Cartan-Hadamard.