On traces of new BMOA type spaces in tubular domains over symmetric cones

We provide new sharp trace theorems in new BMOA type analytic function spaces in tubular domains over symmetric cones under certain condition on the Bergman kernel. We obtain based on known properties of r-lattices in tubular domains complete analogues of our previously known results obtained previously by the authors in the unit ball and then in bounded strongly pseudoconvex domains with smooth boundary. Proofs of all theorems in all domains are based mainly on same ideas.