Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions
Tom 79 / 2002
Annales Polonici Mathematici 79 (2002), 233-264 MSC: Primary 30E05, 46E15. DOI: 10.4064/ap79-3-3
We give an elementary approach which allows us to evaluate Seip's conditions characterizing interpolating and sampling sequences in weighted Bergman spaces of infinite order for a wide class of weights depending on the distance to the boundary of the domain. Our results also give some information on cases not covered by Seip's theory. Moreover, we obtain new criteria for weights to be essential.