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.
| Autores: | , |
|---|---|
| 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 |
| 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. |
|---|