论文标题
单位球上的矢量值伯格曼空间之间的小汉克尔操作员
Little Hankel Operators Between Vector-Valued Bergman Spaces on the Unit Ball
论文作者
论文摘要
在本文中，我们研究了Little Hankel运营商$ H_B $的界限和紧凑性，并在开放单位球$ \ Mathbb {b} _n $ in Blan $ \ Mathbb {c}^n。 \ leq 1，$我们表征那些操作员值符号$ b：\ mathbb {b} _ {n} \ rightarrow \ Mathcal \ Mathcal \ Mathcal {l}（\ edielline {x}，y）$，为此小hankel operator $ h_ p} a^q_α（\ mathbb {b} _ {n}，y），$是一个有界的操作员。另外，给定两个反射复杂的Banach空间$ x，y $和$ 1 <p \ leq q <\ infty，我们表征了那些操作员值的符号$ b：\ mathbb {b} _ {n} \ rightarrow \ rightarrow \ rightarrow \ mathcal \ mathcal {l}（l}（l}（x \ yline {x}，x}，y {by y）$ hankel $ hankEl hankel， a^p_α（\ mathbb {b} _ {n}，x）\ longrightArrow a^q_α（\ mathbb {b} _ {n}，y），$是一个紧凑的操作员。
In this paper, we study the boundedness and the compactness of the little Hankel operators $h_b$ with operator-valued symbols $b$ between different weighted vector-valued Bergman spaces on the open unit ball $\mathbb{B}_n$ in $\mathbb{C}^n.$ More precisely, given two complex Banach spaces $X,Y,$ and $0 < p,q \leq 1,$ we characterize those operator-valued symbols $b: \mathbb{B}_{n}\rightarrow \mathcal{L}(\overline{X},Y)$ for which the little Hankel operator $h_{b}: A^p_α(\mathbb{B}_{n},X) \longrightarrow A^q_α(\mathbb{B}_{n},Y),$ is a bounded operator. Also, given two reflexive complex Banach spaces $X,Y$ and $1 < p \leq q < \infty,$ we characterize those operator-valued symbols $b: \mathbb{B}_{n}\rightarrow \mathcal{L}(\overline{X},Y)$ for which the little Hankel operator $h_{b}: A^p_α(\mathbb{B}_{n},X) \longrightarrow A^q_α(\mathbb{B}_{n},Y),$ is a compact operator.
