Comptes Rendus
no. 5
Mathematical Analysis
Supremum over inverse image of functions in the Bloch space
Jean-Pierre Kahane
Julio C. Ramos Fernández1
1Departamento de Matemática, Universidad de Oriente, 6101 Cumaná, Edo. Sucre, Venezuela
Comptes Rendus. Mathématique, Volume 344 (2007) no. 5, pp. 291-294

We will prove that for certain classes of functions f in the α-Bloch space Bα such that f(0)=0, the Bα norm is obtained taking supremum over f−1(Σε), where Σε={z:|argz|<ε}.

Nous démontrerons que pour certaines classes de fonctions f dans l'espace α-Bloch Bα et telles que f(0)=0, la norme Bα s'obtient comme la borne supérieure sur f−1(Σε), où Σε={z:|argz|<ε}.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.01.013

Julio C. Ramos Fernández  1

1 Departamento de Matemática, Universidad de Oriente, 6101 Cumaná, Edo. Sucre, Venezuela 
Julio C. Ramos Fernández. Supremum over inverse image of functions in the Bloch space. Comptes Rendus. Mathématique, Volume 344 (2007) no. 5, pp. 291-294. doi: 10.1016/j.crma.2007.01.013
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[2] P. Duren Univalent Functions, Springer-Verlag, New York, 1983

[3] D. Marshall; W. Smith The angular distribution of mass by Bergman functions, Rev. Mat. Iberoamericana, Volume 15 (1999), pp. 93-116

[4] F. Pérez-González; J. Ramos Fernández On dominating sets for Bergman spaces, Bergman Spaces and Related Topics in Complex Analysis, Contemp. Math., vol. 404, Amer. Math. Soc., Providence, RI, 2006, pp. 175-185

[5] C. Pommerenke Boundary Behavior of Conformal Maps, Springer-Verlag, 1992

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