The space of bounded analytic functions and weighted Bergman spaces

In this paper, we construct a class of weighted Bergman spaces such that they can generate H-infinity in the sense of Mobius invariance. H-infinity is also equal to the intersection of these spaces. Applying the relation between H-infinity and these spaces, we show that the characterization via higher order derivatives does not hold for some of these weighted Bergman spaces. (C) 2019 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.