The density of the area integral in ${\Bbb R}^{n+1}_+$
The density of the area integral in ${\Bbb R}^{n+1}_+$
Let u(x,y) be a harmonic function in the half-plane R + n+1 , n≥2. We define a family of functionals D(u;r),-∞>r>∞, that are analogs of the family of local times associated to the process u(x t ,y t ) where (x t ,y t ) is Brownian motion in R …