An indestructible Blaschke product in the little Bloch space.

Título inglés An indestructible Blaschke product in the little Bloch space.
Título español Un producto de Blaschke indestructible en el espacio de Bloch pequeño.
Autor/es Bishop, Christopher J.
Organización Dep. Math. State Univ. New York Stony Brook, Stony Brook (New York), Estados Unidos
Revista 0214-1493
Publicación 1993, 37 (1): 95-109, 10 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés The little Bloch space, B0, is the space of all holomorphic functions f on the unit disk such that limlzl→1 lf'(z)l (1- lzl2) = 0. Finite Blaschke products are clearly in B0, but examples of infinite products in B0 are more difficult to obtain (there are now several constructions due to Sarason, Stephenson and the author, among others). Stephenson has asked whether B0 contains an infinite, indestructible Blaschke product, i.e., a Blaschke product B so that (B(z) - a)/(1 - âB(z)), is also a Blaschke product for every element a Î D. In this paper we give an afirmative answer to his question by constructing such a Blaschke product. We also answer a question of Carmona and Cufí by constructing a VMO function, f, so that ll f ll = 1 and whose range set, R(f,a) = {w : there exists zn → a, f(zn) = w}, equals the open unit disk for every a Î T.
Clasificación UNESCO 120209
Palabras clave español Funciones de variable compleja ; Espacios de funciones holomorfas ; Funciones de Bloch
Código MathReviews MR1240926
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