Journal of the
Korean Mathematical Society JKMS

We introduce a new biharmonic kernel for the upper half plane, and then study the properties of its relevant potentials, such as the convergence in the mean and the boundary behavior. Among other things, we shall see that Fatou's theorem is valid for these potentials, so that the biharmonic Poisson kernel resembles the usual Poisson kernel for the upper half plane.

Keywords: Poisson kernel, biharmonic function, biharmonic Green function, convergence in the mean, Fatou's theorem

MSC numbers: 31A30, 31B30, 31A20, 30C40