Hilbert-Schmidt composition operators on Dirichlet spaces



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Gallardo Gutiérrez, Eva A. and González, María J. (2001) Hilbert-Schmidt composition operators on Dirichlet spaces. In Trends in Banach spaces and operator theory. Contemporary mathematics (321). AMS, pp. 87-90. ISBN 978-0-8218-3234-9

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Official URL: http://www.ams.org/books/conm/321/


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.

Item Type:Book Section
Uncontrolled Keywords:composition operator; dirichlet space; weighted Dirichlet space; logarithmic capacity; alpha-capacity
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:21118
Deposited On:26 Apr 2013 10:42
Last Modified:02 Sep 2020 10:15

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