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2 results

  • The Essential Norm of a Bloch-to-${{Q}_{p}}$ Composition Operator

  • Mikael Lindstróm, Shamil Makhmutov, Jari Taskinen
  • Journal:
    Canadian Mathematical Bulletin / Volume 47 / Issue 1 / 01 March 2004
    Published online by Cambridge University Press:
    20 November 2018, pp. 49-59
    Print publication:
    01 March 2004
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  • The ${{Q}_{p}}$ spaces coincide with the Bloch space for $p\,>\,1$ and are subspaces of $\text{BMOA}$ for $0\,<\,p\,\le \,1$. We obtain lower and upper estimates for the essential norm of a composition operator from the Bloch space into ${{Q}_{p}}$, in particular from the Bloch space into $\text{BMOA}$.

  • Composition operators on Qp spaces

  • Part of
  • Zengjian Lou
  • Journal:
    Journal of the Australian Mathematical Society / Volume 70 / Issue 2 / April 2001
    Published online by Cambridge University Press:
    09 April 2009, pp. 161-188
    Print publication:
    April 2001
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  • A holomorphic map ψ of the unit disk ito itself induces an operator Cψ on holomorphic functions by composition. We characterize bounded and compact composition operators Cψ on Qp spaces, which coincide with the BMOA for p = 1 and Bloch spaces for p > 1. We also give boundedness and compactness characterizations of Cψ from analytic function space X to Qp spaces, X = Dirichlet space D, Bloch space B or B0 = {f: f′ ∈ H∞}.