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Journal of Operator Theory

Volume 66, Issue 1, Summer 2011  pp. 145-160}.

Schatten $p$ Class Hankel Operators on the Segal-Bargmann Space $H^2(\mathbb{C}^n, \mathrm d\mu)$ for $0 < p < 1$

Authors J. Isralowitz
Author institution: Mathematics Department, University at Buffalo, Buffalo, 14260, U.S.A.

Summary:  We consider Hankel operators on the Segal-Bargmann space $H^2(\mathbb{C}^n, \mathrm d\mu)$. We obtain necessary and sufficient conditions for the simultaneous membership of $H_f$ and $H_{\overline{f}}$ in the Schatten class $S_p$ for $0 < p < 1$. In particular, we show that the necessary and sufficient conditions obtained by J.~Xia and D. Zheng for the case $1 \leqslant p < \infty$ extend to the case $0 < p < 1$.

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