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Universality on higher order Hardy spaces

Published online by Cambridge University Press:  17 April 2009

L. Bernal-González ,
A. Bonilla  and
M. C. Calderón-Moreno
L. Bernal-González
Affiliation:
Departamento de Análisis Matemático, Facultad de Matematicas, Apdo 1160, Avenida Reina Mercedes, 41080 Sevilla, Spain, e-mail: lbernal@us.es
A. Bonilla
Affiliation:
Departamento de Análisis Matemático, Universidad de la Laguna, C/Astrofísco Fco. Sánchez, s/n, 38271 La Laguna, Spain, e-mail: abonilla@ull.es
M. C. Calderón-Moreno
Affiliation:
Departamento de Análisis Matemático, Facultad de Matematicas, Apdo 1160, Avenida Reina Mercedes, 41080 Sevilla, Spain, e-mail: mccm@us.es
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We prove a Seidel-Walsh-type theorem about the universality of a sequence of derivation-composition operators generated by automorphisms of the unit disk in the setting of the higher order Hardy spaces. Moreover, some related positive or negative assertions involving interpolating sequences and sequences between two tangent circles are established for the class of bounded functions in the unit disk. Our statements improve earlier ones due to Herzog and to the first and third authors.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 1 , February 2005 , pp. 17 - 28
Copyright
Copyright © Australian Mathematical Society 2005

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