RT Journal Article
T1 Locally univalent functions, VMOA and the Dirichlet space
A1 Gallardo Gutiérrez, Eva Antonia
A1 González, María J.
A1 Pérez González, Fernando
A1 Pommerenke, Christian
A1 Rattya, Jouni
AB 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.
PB Oxford University Press (OUP)
SN 0024-6115
YR 2013
FD 2013-03
LK https://hdl.handle.net/20.500.14352/33318
UL https://hdl.handle.net/20.500.14352/33318
LA eng
NO Gallardo Gutiérrez, E.  A., González, M. J., Pérez González, F. et al. «Locally Univalent Functions, VMOA and the Dirichlet Space». Proceedings of the London Mathematical Society, vol. 106, n.o 3, marzo de 2013, pp. 565-88. DOI.org (Crossref), https://doi.org/10.1112/plms/pds040.
NO Plan Nacional I+D
NO Gobierno de Aragon research group Analisis Matematico y Aplicaciones
NO ESF PESC Research Network HCAA
NO Emil Aaltonen Foundation
NO Academy of Finland
DS Docta Complutense
RD 11 abr 2025