On Bergman type projections in new analytic spaces in tubular domains over symmetric cones

We provide new results on the Bergman type projections in products of tubular domains over symmetric cones extending some known classical assertions. Similar results with the same proof may be valid in the Siegel domains and bounded strongly pseudoconvex domains with smooth boundary. Our new Bergman projection theorems may have various interesting applications in function theory in tubular domains over symmetric cones.