Harmonic measure and uniform densities

Details Harmonic measure and uniform densities Harmonic measure and uniform densities

2003-05-05

arxiv.org/abs/math/0305075v1

Indiana Univ. Math. J. 53 (2004), no. 3, 905--923.

Mathematics

Complex Variables

16 pages

Scientific paper

We study two problems concerning harmonic measure on "champagne subdomains" of the unit disk. These domains are obtained by removing from the unit disk little disks around sequences of points with a uniform distribution with respect to the pseudohyperbolic metric of the unit disk. We find (I) a necessary and sufficient condition on the decay of the radii of the little disks for the exterior boundary to have positive harmonic measure, and (II) describe sampling and interpolating sequences for Bergman spaces in terms of the harmonic measure on such ``champagne subdomains''.

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