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.
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Anders Olofsson, Aron Wennman, An operator inequality for weighted Bergman shift operators. Rev. Mat. Iberoam. 29 (2013), no. 3, pp. 789–808DOI 10.4171/RMI/740