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 | References | Similar Articles | Additional Information

Abstract: In this paper we give a complete characterization of higher weight Hankel forms, on the unit ball of , of Schatten-von Neumann class , . 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

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.