Hilbert-Schmidt composition operators on Dirichlet spaces
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2001
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AMS
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Gallardo Gutiérrez, E. A. & González, M. J., Kamińska, A. (ed.). Trends in Banach Spaces and Operator Theory. American Mathematical Society, 2003. DOI.org (Crossref), https://doi.org/10.1090/conm/321.
Abstract
In this note we show that analytic self-maps phi of the unit disk inducing Hilbert-Schmidt composition operators C-phi on the weighted Dirichlet space D-alpha satisfy that the set E-phi = {e(itheta) is an element of partial derivativeD : |phi(e(itheta))| = 1} has zero alpha-capacity.