BOUNDED, COMPACT AND SCHATTEN CLASSES HANKEL OPERATORS ON WEIGHTED FOCK SPACES

  • Chunxu XU
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  • 1. Centre for Mathematics and Science, Hangzhou City University, Hangzhou 310015, China;
    2. School of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, China
Chunxu XU, E-mail: 1968385450@qq.com

Received date: 2024-04-16

  Revised date: 2024-08-15

  Online published: 2025-10-10

Abstract

Let $\phi$ be a smooth radial weight that decays faster than the class Gaussian ones. We obtain certain estimates for the reproducing kernels and the $L^p$-estimates for solutions of the $\overline{\partial}$-equation on the weighted Fock spaces $F_{\phi}^p~(1\leq p\leq\infty)$, which extends the classical Hörmander Theorem. Furthermore, for a suitable $f$, we completely characterize the boundedness and compactness of the Hankel operator $H_f:F_{\phi}^p\rightarrow L^q(\mathbb{C},{\rm e}^{-q\phi(\cdot)}{\rm d}m)$ for all possible $1\leq p,q<\infty$ and also characterize the Schatten-$p$ class Hankel operator $H_f$ from $F_{\phi}^2$ to $L^2(\mathbb{C},{\rm e}^{-2\phi}{\rm d}m)$ for all $0<p<\infty$. As an application, we give a complete characterization of the simultaneously bounded, compact and Schatten-$p$ classes Hankel operators $H_f$ and $H_{\overline{f}}$ on $F_\phi^2$.

Cite this article

Chunxu XU . BOUNDED, COMPACT AND SCHATTEN CLASSES HANKEL OPERATORS ON WEIGHTED FOCK SPACES[J]. Acta mathematica scientia, Series B, 2025 , 45(4) : 1529 -1554 . DOI: 10.1007/s10473-025-0416-z

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