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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Trace class criteria for bilinear Hankel forms of higher weights


Author: Marcus Sundhäll
Journal: Proc. Amer. Math. Soc. 135 (2007), 1377-1388
MSC (2000): Primary 32A25, 32A36, 32A37, 47B32, 47B35.
Published electronically: October 18, 2006
MathSciNet review: 2276646
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Abstract: In this paper we give a complete characterization of higher weight Hankel forms, on the unit ball of $ \mathbb{C}^d$, of Schatten-von Neumann class $ \mathcal{S}_p$, $ 1\leq p\leq \infty$. For this purpose we give an atomic decomposition for certain Besov-type spaces. The main result is then obtained by combining the decomposition and our earlier results.


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Additional Information

Marcus Sundhäll
Affiliation: Department of Mathematics, Chalmers University of Technology and Göteborg University, SE-412 96 Göteborg, Sweden
Email: sundhall@math.chalmers.se

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08583-2
PII: S 0002-9939(06)08583-2
Keywords: Hankel forms, Schatten-von Neumann classes, Bergman spaces, Bergman projections, duality of Besov spaces, atomic decomposition, transvectants, unitary representations, M\"obius group.
Received by editor(s): September 26, 2005
Received by editor(s) in revised form: November 22, 2005
Published electronically: October 18, 2006
Additional Notes: This work is part of the author’s ongoing Ph.D. thesis under the supervision of Yang Liu and Genkai Zhang. He would like to thank Örebro University for the financial support.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.