Comptes Rendus
no. 5
Mathematical Analysis
Supremum over inverse image of functions in the Bloch space
Presented by: 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 
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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

[1] R. Castillo, J. Ramos Fernández, On the angular distribution of mass by Besov functions, B. Belg. Math. Soc. Sim.-St., in press

[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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