Article
Monsters in Hardy and Bergman spaces
Author/s | Bernal González, Luis
Calderón Moreno, María del Carmen |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2002 |
Deposit Date | 2019-06-21 |
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Abstract | 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 ... 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. |
Citation | Bernal González, L. y Calderón Moreno, M.d.C. (2002). Monsters in Hardy and Bergman spaces. Complex Variables, 47 (5), 373-382. |
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