Kelvin transform for α-harmonic functions in regular domains
Krzysztof Michalik, Michał Ryznar · Demonstratio Mathematica · 2012
Abstract We investigate conditional stable processes in a Lipschitz domain D and conditional stable processes in the image of D under the Kelvin transform. We show that, with a suitable change of time, these processes are equal in distribution. As an application, we show the equivalence of the Hardy spaces and the relative Fatou theorem for D and its image.