The Riesz decomposition of finely superharmonic functions

Gardiner SJ, Hansen W. The Riesz decomposition of finely superharmonic functions. Advances in Mathematics. 2007;214(1):417-436.This paper answers a question of Fuglede about minimal positive harmonic functions associated with irregular boundary points. As a consequence, an old and central problem of fine potential theory, concerning the Riesz decomposition, is resolved. Namely, it is shown that, on certain fine domains, there exist positive finely superharmonic functions which do not admit any positive finely harmonic minorant and yet are not fine potentials. (c) 2007 Elsevier Inc. All rights reserved