Fock空间上的小Hankel算子

Small Hankel Operators on Fock Spaces

摘要: 本文主要研究了Fock空间$F_{\alpha }^p$ 上小Hankel算子$h_{\phi }$ 的有界性和紧性，得到了$h_{\phi }$ 在$F_{\alpha }^p$ 上有界的充分必要条件是其符号$\phi$ 属于Fock空间$F_{\frac{\alpha }{2}}^{\infty }$ ；$h_{\phi }$ 在$F_{\alpha }^p$ 上紧的充分必要条件是$\phi$ 属于$f_{\frac{\alpha }{2}}^{\infty }$ 。

Abstract: This paper mainly studies the boundedness and compactness of the small Hankel operator $h_{\phi }$ on Fock space $F_{\alpha }^p$ . It is found that the necessary and sufficient condition for $h_{\phi }$ being bounded on $F_{\alpha }^p$ is that its symbol $\phi$ belongs to Fock space $F_{\frac{\alpha }{2}}^{\infty }$ ; the necessary and sufficient condition for $h_{\phi }$ being compact on $F_{\alpha }^p$ is that $\phi$ belongs to $f_{\frac{\alpha }{2}}^{\infty }$ .