Hankel operators on vector-valued Bergman spaces with exponential weights

Abstract

Let $\mathcal{H}$ be a separable Hilbert space and let $A^{2}_{\varphi}(\mathcal{H})$ be the $\mathcal{H}$-valued Bergman spaces with exponential weights. In the present paper, we give the complete characterizations for the boundedness and compactness of Hankel operators on $A^{2}_{\varphi}(\mathcal{H})$. For $p\geq2$, the Schatten $p$-classes of the Hankel operator with conjugate analytic symbols are studied.