On some new estimates related with Bergman ball and Poisson integral in tubular domain and unit ball

We introduce new Herz type analytic spaces based on Bergman balls in tubular domains over symmetric cones and in products of such type domains. We provide for these Herz type spaces new maximal and embedding theorems extending known results in the unit disk. In addition we define new Poisson-type integral in the unit ball and extend a known classical maximal theorem related with it. Related results for such type integrals will be given.