arXiv subjects
Publications and source records attributed to Satoshi Yamaji.
Using an integral formula on a homogeneous Siegel domain, we show a necessary and sufficient condition for composition operators on the weighted Bergman space of a minimal bounded homogeneous domain to be compact. To describe the compactness of composition operators, we see a boundary behavior of the Bergman kernel.
We describe the Bergman kernel of any bounded homogeneous domain in a minimal realization relating to the Bergman kernels of the Siegel disks. Taking advantage of this expression, we obtain substantial estimates of the Bergman kernel of the homogeneous domain.
Necessary and sufficient conditions for positive Toeplitz operators on the Bergman space of a minimal bounded homogeneous domain to be bounded or compact are described in terms of the Berezin transform, the averaging function and the Carleson property.