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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Communicated by Daniel Aron Alpay.
This work was supported by scholarships from NSERC (Canada) and FQRNT (Québec) and is part of the author’s doctoral dissertation.
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Guillot, D. Fine Boundary Behavior and Invariant Subspaces of Harmonically Weighted Dirichlet Spaces. Complex Anal. Oper. Theory 6, 1211–1230 (2012). https://doi.org/10.1007/s11785-010-0124-z
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DOI: https://doi.org/10.1007/s11785-010-0124-z