Journal of Operator Theory
Volume 66, Issue 1, Summer 2011 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 $0 < p < 1$.
Keywords: Schatten class, Hankel operators, Segal--Bargmann space
Contents
Full-Text PDF