Riesz measure of functions that are subharmonic in the exterior of a compact (Q486897)

Let \(E\subset\mathbb R^m\) be a compact \(r\)-convex set, and \(m>2\). Let \(v\) be a subharmonic function in \(\Omega =\mathbb R^m \setminus E\). Denote \(\mu =\Delta v\). Let \(\varphi \), \(\psi \) be continuous positive functions on \((0,\infty )\) such that \(v(x)\leq \varphi (\text{dist} (x,E))\). Under some conditions on \(\varphi \) and \(\psi \) the authors prove an integral inequality for \(\psi \) and \(\mu \).