%0 Book Section %T Hilbert-Schmidt composition operators on Dirichlet spaces publisher AMS %D 2001 %U 978-0-8218-3234-9 %@ https://hdl.handle.net/20.500.14352/60676 %X 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. %~