Harmonic measure and uniform densities

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2004Embargo end date: 01 May 2003 Spain English Publisher:Indiana University Mathematics JournalJournal:Indiana University Mathematics Journal, volume 53, pages 905-924 (issn: 0022-2518,

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Authors: Ortega Cerdà, Joaquim; Seip, Kristian;

doi: 10.1512/iumj.2004.53.2467 , 10.48550/arxiv.math/0305075

arXiv: math/0305075

handle: 2445/164723

Harmonic measure and uniform densities

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Abstract

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''.

16 pages

Country

Spain

Related Organizations

University of Barcelona
Spain
Norwegian University of Science and Technology
Norway

Keywords

Harmonic functions, Mathematics - Complex Variables, Geometric function theory, Capacity and harmonic measure in the complex plane, Potential theory (Mathematics), 30C85, 31C05, Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions, harmonic measure, pseudohyperbolic distance, uniform density, interpolating sequence, Teoria del potencial (Matemàtica), Mathematics - Classical Analysis and ODEs, Teoria geomètrica de funcions, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Spaces of bounded analytic functions of one complex variable, Funcions harmòniques, Blaschke product, Complex Variables (math.CV)

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