Compactness of Hankel and Toeplitz operators on convex Reinhardt domains in $\mathbb{C}^2$
Complex Variables
2025-07-24 v2 Functional Analysis
Abstract
We study compactness of Hankel and Toeplitz operators on Bergman spaces of convex Reinhardt domains in and we restrict the symbols to the class of functions that are continuous on the closure of the domain. We prove that Toeplitz operators as well as the Hermitian squares of Hankel operators are compact if and only if the Berezin transforms of the operators vanish on the boundary of the domain.
Keywords
Cite
@article{arxiv.2501.02339,
title = {Compactness of Hankel and Toeplitz operators on convex Reinhardt domains in $\mathbb{C}^2$},
author = {Nazli Dogan and Sonmez Sahutoglu},
journal= {arXiv preprint arXiv:2501.02339},
year = {2025}
}
Comments
minor editorial changes; to appear in Banach J. Math. Anal