On Lp solutions to the Laplace equation and zeros of holomorphic functions

Abstract

The problem we solve in this paper is to characterize, in a smooth domain $\Omega$ in $\mathbb{R}^{n}$ and for $1 \leq p \leq \infty,$ those positive Borel measures on $\Omega$ for which there exists a subharmonic function $u \in L^{p}(\Omega)$ such that $\Delta u=\mu$.