Hankel operators in the Bergman space and Schatten $p$-classes: The case $1<p<2$
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- by Jingbo Xia PDF
- Proc. Amer. Math. Soc. 129 (2001), 3559-3567 Request permission
Abstract:
K. Zhu proved in Amer. J. Math. 113 (1991), 147-167, that, for $2 \leq p < \infty$, the Hankel operators $H_{f}$ and $H_{\bar f}$ on the Bergman space belong to the Schatten class ${\mathcal {C}}_{p}$ if and only if the mean oscillation MO$(f)(z)= \{\widetilde {|f|^{2}}(z) - |\tilde f(z)|^{2}\}^{1/2}$ belongs to $L^{p}(D,(1-|z|^{2})^{-2}dA(z))$. In this paper we prove that the same result also holds when $1 < p < 2$.References
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Additional Information
- Jingbo Xia
- Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260
- MR Author ID: 215486
- Email: jxia@acsu.buffalo.edu
- Received by editor(s): April 11, 2000
- Published electronically: May 21, 2001
- Additional Notes: This work was supported in part by NSF grant DMS-9703515.
- Communicated by: Joseph A. Ball
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 3559-3567
- MSC (2000): Primary 47B10, 47B32, 47B35
- DOI: https://doi.org/10.1090/S0002-9939-01-06217-7
- MathSciNet review: 1860488