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