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...

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Detalles Bibliográficos
Autores: Bernal González, Luis, Calderón Moreno, María del Carmen
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
Descripción
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.