HANKEL BILINEAR FORMS ON GENERALIZEDFOCK SOBOLEV SPACES ON Cn

摘要

We characterize the boundedness of Hankel bilinear forms on a product of generalized Fock Sobolev spaces on Cnwith respect to the weight (1 + |z|)sup>e-/2|z|^{2l}, for l 1, > 0 and R.We obtain a weak decomposition of the Bergman kernel with estimates and a Littlewood Paley formula, which are key ingredients in the proof of our main results.As an application, we characterize the boundedness, compactness and the membership in the Schatten class of small Hankel operators on these spaces.