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

Published online by Cambridge University Press:  20 November 2018

Marcus Sundhäll  and
Edgar Tchoundja
Marcus Sundhäll
Affiliation:
Mathematical Institute, Silesian University in Opava, Na Rybnicku 1, CZ-746 01, Czech Republic, e-mail: Marcus.Sundhall@oru.se
Edgar Tchoundja
Affiliation:
Department of Mathematical Sciences, Division of Mathematics, Chalmers University of Technology and Göteborg University, SE-412 96 Göteborg, Sweden, e-mail: etchoundja@crm.cat
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Abstract

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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

32A2532A3532A3747B35Hankel formsSchatten–von Neumann classesBergman spacesHardy spacesBesov spacestransvectantsunitary representationsMöbius group
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 62 , Issue 2 , 01 April 2010 , pp. 439 - 455
Copyright
Copyright © Canadian Mathematical Society 2010

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