Projection theorems for harmonic measure in NTA domains (Q1841546)

Let \(D\) be an NTA domain, and \(E\subset D\) be a closed subset. It is assumed that there exists a kind of projection \(P^{x_0}(E)\), depending on a fixed point \(x_0\), of \(E\) onto the boundary of \(D\). The projection is a sort of generalization of the radial projection. The main result of this paper is that the harmonic measure of the set \(\partial E\) with respect to the domain \(D\setminus E\) can be estimated from below with the harmonic measure of the set \(P^{x_0}(E)\) times a constant which is independent of \(E\) but depending on \(x_0\).