A converse Fatou theorem (Q1262410)

Using a translation invariant pseudo-metric on \({\mathbb{R}}^ n\) the authors define ``locally admissible'' regions. They consider functions \(K\mu (x,t)=\int_{{\mathbb{R}}^ n}K_ t(x-y)\mu (dy)\) where each \(K_ t\), \(t>0\), is a nonnegative function on \({\mathbb{R}}^ n\) satisfying certain conditions (which are valid for the kernels appearing in the integral representation of the positive solutions of Laplace's equation and certain parabolic equations). They show that a Fatou theorem holds exactly for an approach within locally admissible sets.