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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