Nontangential Limits and Nontangetial Boundedness for Solutions of Hermite Type Equations

Abstract

Nontangential convergence on the boundary is studied for L-harmonic functions defined on the upper half-space, where L is either a slightly more general operator than the Hermite operator or is a perturbation of the classical Laplacian. In addition, the Poisson kernel and the Poisson integral associated with L are analyzed in detail and several properties of independent interest are presented.