scholarly journals Interpolating Sequences in Spaces with the Complete Pick Property

2017 ◽  
Vol 2019 (12) ◽  
pp. 3832-3854 ◽  
Author(s):  
Alexandru Aleman ◽  
Michael Hartz ◽  
John E McCarthy ◽  
Stefan Richter
Keyword(s):  
Hardy Space ◽  
Carleson Measure ◽  
Hilbert Function ◽  
Dirichlet Space ◽  
Function Spaces ◽  
Interpolating Sequences ◽  
Hilbert Function Spaces ◽  
Multiplier Algebras

Abstract We characterize interpolating sequences for multiplier algebras of spaces with the complete Pick property. Specifically, we show that a sequence is interpolating if and only if it is separated and generates a Carleson measure. This generalizes results of Carleson for the Hardy space and of Bishop, Marshall, and Sundberg for the Dirichlet space. Furthermore, we investigate interpolating sequences for pairs of Hilbert function spaces.

scholarly journals The n-th derivative characterisation of Möbius invariant Dirichlet space

1998 ◽  
Vol 58 (1) ◽  
pp. 43-56 ◽  
Author(s):  
Rauno Aulaskari ◽  
Maria Nowak ◽  
Ruhan Zhao
Keyword(s):  
Carleson Measure ◽  
Bloch Space ◽  
Dirichlet Space ◽  
Function Spaces ◽  
Multiplier Space ◽  
Little Bloch Space ◽  
Special Parameter

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.

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