Continuous Functions and Riesz Type Potentials in Homogeneous Spaces

We develop a potential theory for a Riesz type kernel in a homogeneous space and characterize the compact sets K with capacity zero as the sets K for which every continous function f on K is the restriction to K of a continuous potential of an absolutely continuous measure sigma (f) supported in an arbitrarily small neighbourhood of K. The measure sigma (f) can be choosen as a suitable restriction of a single measure sigma that only depends on the set K and the kernel k.