Hilbert-Schmidt composition operators on Dirichlet spaces

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.

Detalles Bibliográficos
Autores: Gallardo Gutiérrez, Eva Antonia, González, María J.
Tipo de recurso: capítulo de libro
Fecha de publicación:2001
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/60676
Acceso en línea:https://hdl.handle.net/20.500.14352/60676
Access Level:acceso abierto
Palabra clave:517
Composition operator
Dirichlet space
Weighted Dirichlet space
Logarithmic capacity
Alpha-capacity
Análisis matemático
1202 Análisis y Análisis Funcional
Descripción
Sumario: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.