Preprint MA 59/2007

On Hankel forms of higher weights, the case of Hardy spaces

Marcus Sundhäll and Edgar Tchoundja

In this paper we study bilinear Hankel forms of higher weights on Hardy spaces in several dimensions (Hankel forms of higher weights on weighted Bergman spaces have already been studied by Sundhäll). We get a full characterization of Schatten class Hankel forms in terms of the membership for the symbols to be in certain Besov spaces. Also, the Hankel forms are bounded and compact if and only if their corresponding symbols satisfy certain Carleson measure criteria and vanishing Carleson measure criteria, respectively.