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arXiv · 2012.10934

Little Hankel Operators Between Vector-Valued Bergman Spaces on the Unit Ball

David Békollé·Hugues Olivier Defo·Edgar L. Tchoundja·Brett D. Wick
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Abstract

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 $h_{b}: A^p_{\alpha}(\mathbb{B}_{n},X) \longrightarrow A^q_{\alpha}(\mathbb{B}_{n},Y),$ 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 $h_{b}: A^p_{\alpha}(\mathbb{B}_{n},X) \longrightarrow A^q_{\alpha}(\mathbb{B}_{n},Y),$ is a compact operator.

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BibTeXRIS

David Békollé, Hugues Olivier Defo, Edgar L. Tchoundja, Brett D. Wick. 2020-12-20. Little Hankel Operators Between Vector-Valued Bergman Spaces on the Unit Ball. https://arxiv.org/abs/2012.10934

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