An operator inequality for weighted Bergman shift operators

  • Anders Olofsson

    Lund University, Sweden
  • Aron Wennman

    Royal Institute of Technology, Stockholm, Sweden


We prove an operator inequality for the Bergman shift operator on weighted Bergman spaces of analytic functions in the unit disc with weight function controlled by a curvature parameter assuming nonnegative integer values. This generalizes results by Shimorin, Hedenmalm and Jakobsson concerning the cases and . A naturally derived scale of Hilbert space operator inequalities is studied and shown to be relaxing as the parameter increases. Additional examples are provided in the form of weighted shift operators.

Cite this article

Anders Olofsson, Aron Wennman, An operator inequality for weighted Bergman shift operators. Rev. Mat. Iberoam. 29 (2013), no. 3, pp. 789–808

DOI 10.4171/RMI/740