Hankel operators on Bergman spaces of tube domains over symmetric cones (Q733625)

Let \(\Omega\) be an irreducible symmetric cone in \({\mathbb R}^n\) and \(T_\Omega\) be a corresponding tube domain in \({\mathbb C}^n\). The small Hankel operator \(h_b\) on the Bergman space \(A^2(T_\Omega)\) with symbol \(b\) is defined as \(h_b(f)=P(b\overline{f})\), where \(P\) is the Bergman projection. The main result of the paper says that, if \(b\) is analytic and \(1\leq p\leq\infty\), then \(h_b\) belongs to the Schatten class \({\mathcal S}_p\) if and only if \(b\) belongs to the Besov space \({\mathcal B}^p\).