Gallardo Gutiérrez, Eva AntoniaGonzález, María J.Kaminska, Anna2023-06-202023-06-202001Gallardo 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/321.978-0-8218-3234-910.1090/conm/321https://hdl.handle.net/20.500.14352/60676In 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.engbook parthttps//doi.org/10.1090/conm/321http://www.ams.org/books/conm/321/open access517Composition operatorDirichlet spaceWeighted Dirichlet spaceLogarithmic capacityAlpha-capacityAnálisis matemático1202 Análisis y Análisis Funcional