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2004

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/164723

Harmonic measure and uniform densities

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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'.

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https://doi.org/10.1512/iumj.2004.53.2467

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Teoria geomètrica de funcions, Funcions harmòniques, Teoria del potencial (Matemàtica)

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Geometric function theory, Harmonic functions, Potential theory (Mathematics)

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ORTEGA CERDÀ, Joaquim and SEIP, Kristian. Harmonic measure and uniform densities. Indiana University Mathematics Journal. 2004. Vol. 53, num. 3, pags. 905-923. ISSN 0022-2518. [consulted: 16 of October of 2026]. Available at: https://hdl.handle.net/2445/164723

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