Bergman-Lorentz spaces on tube domains over symmetric cones

Abstract

We study Bergman-Lorentz spaces on tube domains over symmetric cones, i.e. spaces of holomorphic functions which belong to Lorentz spaces $L(p, q).$ We establish boundedness and surjectivity of Bergman projectors from Lorentz spaces to the corresponding Bergman-Lorentz spaces and real interpolation between Bergman-Lorentz spaces. Finally we ask a question whose positive answer would enlarge the interval of parameters $p\in (1, \infty)$ such that the relevant Bergman projector is bounded on $L^p$ for cones of rank $r\geq 3.$