Fine Boundary Behavior and Invariant Subspaces of Harmonically Weighted Dirichlet Spaces |
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| Authors: | Dominique Guillot |
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| Affiliation: | 1. D??partement de math??matiques et de statistique, Pavillon Alexandre-Vachon, Universit?? Laval, 1045, avenue de la M??decine, Qu??bec, QC, G1V 0A6, Canada
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| Abstract: | We study the boundary behavior of functions in spaces of Dirichlet-type by using non-linear capacities generalizing the logarithmic capacity. We use these capacities to obtain information about the invariant subspaces of the shift operator. As an application, we prove an analogue of a conjecture of Brown and Shields when the space is weighted by the Poisson integral of a finite sum of atoms. |
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