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, ∞) such that the relevant Bergman projector is bounded on L^p for cones of rank r greater than or equal to 3.

The authors wish to express their gratitude to Aline Bonami, Jacques Faraut, Gustavo Garrigós and Chokri Yacoub for valuable discussions. They are indebted to Michael Cwikel for pointing out section 3 of [16], which provided the proof of Theorem 5.5. They also thank the referee for his (her) thorough reading of the manuscript and his (her) many useful suggestions.