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The n-th derivative characterisation of Möbius invariant Dirichlet space

  • Rauno Aulaskari (a1), Maria Nowak (a2) and Ruhan Zhao (a3)
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.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[5] R. Aulaskari , D. A. Stegenga and J. Xiao , ‘Some subclasses of BMOA and their characterization in terms of Carleson measures’, Rocky Mountain J. Math. 26 (1996), 485506.

[6] R. Aulaskari , J. Xiao and R. Zhao , ‘On subspaces and subsets of BMOA and UBC’, Analysis 15 (1995), 101121.

[7] S. Axler , ‘The Bergman space, the Bloch space and commutators of multiplication operators’, Duke Math. J. 53 (1986), 315332.

[11] M. Mateljevic and M. Pavlovic , ‘Multipliers of Hp and BMOA’, Pacific J. Math. 146 (1990), 7184.

[16] J. Xiao and L. Zhong , ‘On little Bloch space, atomic decomposition and free interpolation’, Complex Variables Theory Appl. 27 (1995), 175184.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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