@Article{ATA-39-105,
author = {Dong , Xingtang and Feng , Li},
title = {Characterizations of Bounded Singular Integral Operators on the Fock Space and Their Berezin Transforms},
journal = {Analysis in Theory and Applications},
year = {2023},
volume = {39},
number = {2},
pages = {105--119},
abstract = {<p style="text-align: justify;">There is a singular integral operators $S_{\varphi}$ on the Fock space $\mathcal{F}^2(\mathbb{C}),$ which originated from the unitarily equivalent version of the Hilbert transform on $L^2(\mathbb{R}).$ In this paper, we give an analytic characterization of functions $\varphi$ with finite zeros such that the integral operator $S_{\varphi}$ is bounded on $\mathcal{F}^2(\mathbb{C})$ using Hadamard’s factorization theorem. As an application, we obtain a complete characterization for such symbol functions $\varphi$ such that the Berezin transform of $S_{\varphi}$ is bounded while the operator $S_{\varphi}$ is not. Also, the corresponding problem in higher dimensions is considered.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.OA-2021-0034},
url = {http://global-sci.org/intro/article_detail/ata/21818.html}
}