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# On Hankel Forms of Higher Weights: The Case of Hardy Spaces

Published:2009-12-04
Printed: Apr 2010
• Marcus Sundhäll
• Edgar Tchoundja
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## Abstract

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 Sundhäll 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, Schatten—von Neumann classes, Bergman spaces, Hardy spaces, Besov spaces, transvectant, unitary representations, Möbius group
 MSC Classifications: 32A25 - Integral representations; canonical kernels (Szegoo, Bergman, etc.) 32A35 - $H^p$-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15] 32A37 - Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) [See also 46Exx] 47B35 - Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]

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