Czechoslovak Mathematical Journal, Vol. 74, No. 4, pp. 1241-1263, 2024
Stević-Sharma type operators on Fock spaces in several variables
Lijun Ma, Zicong Yang
Received June 14, 2024. Published online September 18, 2024.
Abstract: Let $\varphi$ be an entire self-map of $\mathbb{C}^N$, $u_0$ be an entire function on $\mathbb{C}^N$ and $ u=(u_1,\cdots,u_N)$ be a vector-valued entire function on $\mathbb{C}^N$. We extend the Stević-Sharma type operator to the classcial Fock spaces, by defining an operator $T_{u_0, u,\varphi}$ as follows: $T_{u_0, u,\varphi}f=u_0\cdot f\circ\varphi+\sum_{i=1}^Nu_i\cdot\frac{\partial f}{\partial z_i}\circ\varphi.$ We investigate the boundedness and compactness of $T_{u_0, u,\varphi}$ on Fock spaces. The complex symmetry and self-adjointness of $T_{u_0, u,\varphi}$ are also characterized.
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Affiliations: Lijun Ma, Zicong Yang (corresponding author), Department of Mathematics, Hebei University of Technology, No. 5340, Xiping Road, Beichen District, Tianjin 300401, China e-mail: mljzsu@163.com, zc25@hebut.edu.cn
