Gallardo Gutiérrez, Eva AntoniaGonzález, María J.Pérez González, FernandoPommerenke, ChristianRattya, Jouni2023-06-192023-06-192013-03Gallardo 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/pds040.0024-611510.1112/plms/pds040https://hdl.handle.net/20.500.14352/33318We 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.engjournal articlehttps//doi.org/10.1112/plms/pds040http://plms.oxfordjournals.org/content/106/3/565.full.pdf+htmlopen access517.5Bounded mean oscillationSchlicht functionsAnalytic-functionsFunciones (Matemáticas)1202 Análisis y Análisis Funcional