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Title: Harmonic measure and uniform densities
Author: Ortega Cerdà, Joaquim
Seip, Kristian
Keywords: Teoria geomètrica de funcions
Funcions harmòniques
Teoria del potencial (Matemàtica)
Geometric function theory
Harmonic functions
Potential theory (Mathematics)
Issue Date: 2004
Publisher: Indiana University
Abstract: We study two problems concerning harmonic measure on certain 'champagne subdomains' of the unit disk $\D$. The domains that we consider are obtained by removing from $\D$ little disks around sequences of points with a uniform distribution with respect to the pseudohyperbolic metric of $\D$. 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'.
Note: Versió preprint del document publicat a:
It is part of: Indiana University Mathematics Journal, 2004, vol. 53, num. 3, p. 905-923
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ISSN: 0022-2518
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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