A subordination Principle. Applications

The subordination principle states roughly : if a property is true for Hardy spaces in some kind of domains in $C^n$ then it is also true for the Bergman spaces of the same kind of domains in $C^{n-1}$. We give applications of this principle to Bergman-Carleson measures, interpolating sequences for Bergman spaces, $A^p$ Corona theorem and characterization of the zeros set of Bergman-Nevanlinna class.