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The n-th derivative characterisation of Möbius invariant Dirichlet space

Published online by Cambridge University Press:  17 April 2009

Rauno Aulaskari ,
Maria Nowak  and
Ruhan Zhao
Rauno Aulaskari
Affiliation:
University of Joensuu, PO Box 111, FIN-8010 Joensuu, Finland e-mail: [email protected]
Maria Nowak
Affiliation:
Institute of Mathematics, Maria Curie-Sklodowska University, pl. M. Curie-Skodowskiej 1, 20–031 Lublin, Poland
Ruhan Zhao
Affiliation:
University of Joensuu, PO Box 111, FIN-8010 Joensuu, Finland
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Abstract

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In this paper we give the n-th derivative criterion for functions belonging to recently defined function spaces Qp and Qp, 0. For a special parameter value p = 1 this criterion is applied to BMOA and VMOA, and for p > 1 it is applied to the Bloch space and the little Bloch space . Further, a Carleson measure characterisation is given to Qp, and in the last section the multiplier space from Hq into Qp is considered.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 58 , Issue 1 , August 1998 , pp. 43 - 56
Copyright
Copyright © Australian Mathematical Society 1998

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