Complex Interpolation Between Two Mixed Norm Bergman Spaces in Tube Domains Over Homogeneous Cones

We use a family of atomic decomposition operators to determine an explicit function realising the complex interpolation between two mixed norm weighted Bergman spaces in tube domains over open convex homogneous cones. Our results extend and improve earlier work from (Békollé et al. in C R Acad Sci Paris Ser I(337):13–18, 2003), where the problem was considered for scalar powers α = ( α , … , α ) and symmetric cones Ω .