Densité de l'intégrale d'aire dans \({\mathbb{R}}_+^{n+1}\) et limites non tangentielles. (Density of the area integral in \({\mathbb{R}}_ +^{n+1}\) and non-tangential limits)
Let u be a harmonic function in the half space \({\mathbb{R}}_+^{n+1}\). Let \(r\mapsto D\) r be the density of the area integral associated with u. The two main results of this paper are: -- A continuity property of the application \(r\mapsto D^ r\) (the analytic analogue of Trotter's theorem on the continuity of the local time associated with a martingale). -- A criterion for u to have a non-tangential limit, using the density of the area integral.
scientific article; zbMATH DE number 4069286