Monsters in Hardy and Bergman spaces
A monster in the sense of Luh is a holomorphic function on a simply connected domain in the complex plane such that it and all its derivatives and antiderivatives exhibit an extremely wild behaviour near the boundary. In this paper the Hardy spaces Hp and the Bergman spaces Bp (1 ≤ p < ∞) on the...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2002 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/87540 |
| Acceso en línea: | https://hdl.handle.net/11441/87540 https://doi.org/10.1080/02781070290013839 |
| Access Level: | acceso abierto |
| Palabra clave: | Luh-monster T-monster Hardy space Bergman space Strongly omnipresent operator Differential operator Hypercyclic function |
| Sumario: | A monster in the sense of Luh is a holomorphic function on a simply connected domain in the complex plane such that it and all its derivatives and antiderivatives exhibit an extremely wild behaviour near the boundary. In this paper the Hardy spaces Hp and the Bergman spaces Bp (1 ≤ p < ∞) on the unit disk are considered, and it is shown that there are no Luh-monsters in them. Nevertheless, it is proved that T-monsters (as introduced by the authors in an earlier work) can be found in each of these spaces for any finite order linear differential operator T. |
|---|