文摘
We consider Hankel operators H[`(f)]H_{\bar{f}} with antiholomorphic symbol [`(f)]\bar{f} on the generalized Fock space A2(mm){\mathcal{A}}^{2}(\mu_{m}) , where μ m is the measure with weight e-|z|me^{{-|z|}^{m}} , m > 0 with respect to the Lebesgue measure in \mathbbCn{\mathbb{C}}^{n} . We prove that H[`(f)]H_{\bar{f}} is bounded if and only if f is a polynomial of degree at most \fracm2\frac{m}{2} . We show that H[`(f)]H_{\bar{f}} is compact if and only if f is a polynomial of degree strictly smaller that \fracm2\frac{m}{2} . We also establish that H[`(f)]H_{\bar{f}} is in the Schatten class Sp{\mathcal{S}}_{p} if and only if p > 2n and f is a polynomial of degree strictly smaller than m\frac(p-2n)2pm\frac{(p-2n)}{2p} .