Locally univalent functions, VMOA and the Dirichlet space
We study geometric properties of the image of the unit circle under a bounded locally univalent function g such that log g' belongs either to the Dirichlet space D, VMOA or the little Bloch space B-0. Concerning VMOA and B-0, our findings generalize the corresponding results for conformal maps...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/33318 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/33318 |
| Access Level: | acceso abierto |
| Palabra clave: | 517.5 Bounded mean oscillation Schlicht functions Analytic-functions Funciones (Matemáticas) 1202 Análisis y Análisis Funcional |
| Sumario: | We study geometric properties of the image of the unit circle under a bounded locally univalent function g such that log g' belongs either to the Dirichlet space D, VMOA or the little Bloch space B-0. Concerning VMOA and B-0, our findings generalize the corresponding results for conformal maps shown by Pommerenke in the late 1970s. In the case of D, we give a strictly geometric necessary condition for g to satisfy log g'is an element of D, and also offer two different 'semi-geometric' characterizations of when log g'is an element of D. |
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