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The rank of Hankel operators on harmonic Bergman spaces

Author(s): Lova Zakariasy
Journal: Proc. Amer. Math. Soc. 131 (2003), 1177-1180.
MSC (2000): Primary 47B35
Posted: November 4, 2002
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Abstract: We show that on the harmonic Bergman spaces, the Hankel operators with nonconstant harmonic symbol cannot be of finite rank.

References:

1.: N. Das, The kernel of a Hankel operator on the Bergman space, Bull. London Math. Soc. 31 (1999), 75-80. MR 99j:47034
2.: M. Jovovic, Compact Hankel operators on Harmonic Bergman spaces, Integral Equations Operator Theory, Vol. 22, 1995, 295-304. MR 96d:47031
3.: E. Strouse, Finite rank intermediate Hankel operators, Arch. Math. (Basel), Vol. 67, 1996, 142-149. MR 97i:47047
4.: Z. Wu, Operators on harmonic Bergman spaces, Integral Equations Operator Theory, Vol. 24, 1996, 352-371. MR 97c:47028

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Additional Information:

Lova Zakariasy
Affiliation: Department of Mathematics, University of Bordeaux I, 351, cours de la Liberation, 33045 Talence cedex, France
Email: lova.zakariasy@math.u-bordeaux.fr

DOI: 10.1090/S0002-9939-02-06638-8
PII: S 0002-9939(02)06638-8
Keywords: Hankel operators, harmonic Bergman spaces
Received by editor(s): September 14, 2001
Received by editor(s) in revised form: November 11, 2001
Posted: November 4, 2002
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2002, American Mathematical Society


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