Riesz decomposition for superbiharmonic functions in the unit ball

Abstract

For a superbiharmonic function $u$ in the unit ball with the growth condition of spherical means, we show that $u$ is represented as the sum of a generalized Riesz potential and a biharmonic function. This representation is referred to as Riesz decomposition for superbiharmonic functions. \\ ~~~The superharmonic case is treated similarly.