Generalized interpolation in Bergman spaces and extremal functions

In a recent paper A. SCHUSTER and K. SEIP [SchS] have characterized interpo lating sequences for Bergman spaces in terms of extremal functions (or cano nical divisors). As these are natural analogues in Bergman spaces of Blasch ke products, this yields a Carleson type condition for interpolation. We in tend to generalize this idea to generalized free interpolation in weighted Bergman spaces B-p,B-alpha as was done by V. VASYUNIN [Va1] and N. NIKOLSKI [Ni1] (cf. also [Ha2]) in the case of Hardy spaces. In particular we get a strong necessary condition for free interpolation in B-p,B-alpha On zero- sets of B-p,B-alpha-functions that in the special case of finite unions of B-p,B-alpha-interpolating sequences turns out to be also sufficient.