On harmonic Bloch-type mappings
Let f be a complex-valued harmonic mapping defined in the unit disk (Formula presented.). We introduce the following notion: we say that f is a Bloch-type function if its Jacobian satisfies (Formula presented.) This gives rise to a new class of functions which generalizes and contains the well-known...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universidad Autónoma de Madrid |
| Repositorio: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.uam.es:10486/710202 |
| Acceso en línea: | http://hdl.handle.net/10486/710202 |
| Access Level: | acceso abierto |
| Palabra clave: | Bloch functions coefficient estimates growth estimates harmonic functions Jacobian schlicht radius univalent functions Matemáticas |
| Sumario: | Let f be a complex-valued harmonic mapping defined in the unit disk (Formula presented.). We introduce the following notion: we say that f is a Bloch-type function if its Jacobian satisfies (Formula presented.) This gives rise to a new class of functions which generalizes and contains the well-known analytic Bloch space. We give estimates for the schlicht radius, the growth and the coefficients of functions in this class. We establish an analogue of the theorem which, roughly speaking, states that for ϕ analytic ϕ' is Bloch if and only if ϕ is univalent |
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