Lebesgue mixed norm estimates for Bergman projectors: from tube domains over homogeneous cones to homogeneous Siegel domains of type II

摘要

We present a transference principle of Lebesgue mixed norm estimates forBergman projectors from tube domains over homogeneous cones to homogeneousSiegel domains of type II associated to the same cones. This principle impliesimprovements of these estimates for homogeneous Siegel domains of type IIassociated with Lorentz cones, e.g. the Pyateckii-Shapiro Siegel domain of typeII.