The n-th derivative characterisation of Möbius invariant Dirichlet space

Author:

Aulaskari Rauno,Nowak Maria,Zhao Ruhan

Abstract

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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference18 articles.

1. Some results on Qp spaces, 0 < p < 1;Essén;J. Reine Angew. Math.,1997

2. Some Subclasses of BMOA and their Characterization in Terms of Carleson Measures

3. Möbius invariant function spaces;Arazy;J. Reine Angew. Math.,1985

4. On entire functions, Bloch and normal functions;Aulaskari;Chinese Ann. Math. Ser. B,1996

5. Multipliers of Dirichlet space;Stegenga;Illinois J. Math.,1980

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