On BMO property for potentials on Riemann surfaces (Q913033)

The author studies the BMO property for potentials. First, he gives a characterization of a measure \(\mu\) for which the Newtonian potential belongs to \(BMO({\mathbb{R}}^ n)\). A similar characterization is also valid for Riesz potentials. Next, the author investigates BMO property for potentials on the unit disk D. The following two BMO spaces are introduced: (i) BMO(D,m), the BMO space in the usual sense, (ii) BMO(D,\(\lambda)\), the BMO space with respect to the hyperbolic measure on D. The author gives a characterization of a measure \(\mu\) on D for which the Green potential belongs to BMO(D,m). He also shows that every Dirichlet function on D belongs to BMO(D,\(\lambda)\).