1. CJM 2009 (vol 62 pp. 439)
|On Hankel Forms of Higher Weights: The Case of Hardy Spaces|
In this paper we study bilinear Hankel forms of higher weights on Hardy spaces in several dimensions. (The Schatten class Hankel forms of higher weights on weighted Bergman spaces have already been studied by Janson and Peetre for one dimension and by SundhÃ¤ll for several dimensions). We get a full characterization of Schatten class Hankel forms in terms of conditions for the symbols to be in certain Besov spaces. Also, the Hankel forms are bounded and compact if and only if the symbols satisfy certain Carleson measure criteria and vanishing Carleson measure criteria, respectively.
Keywords:Hankel forms, Schattenâvon Neumann classes, Bergman spaces, Hardy spaces, Besov spaces, transvectant, unitary representations, MÃ¶bius group
Categories:32A25, 32A35, 32A37, 47B35