@Article{CMR-39-3,
author = {Zu, Chao and Yixin, Yang and Yufeng, Lu},
title = {Hilbert-Schmidtness of Submodules in $H^2 (\mathbb{D}^2 )$ Containing $θ(z)−\varphi (w)$},
journal = {Communications in Mathematical Research },
year = {2023},
volume = {39},
number = {3},
pages = {331--341},
abstract = {<p style="text-align: justify;">A closed subspace $M$ of the Hardy space $H^2(\mathbb{D}^2)$ over the bidisk is called submodule if it is invariant under multiplication by coordinate functions $z$ and $w.$ Whether every finitely generated submodule is Hilbert-Schmidt is an unsolved problem. This paper proves that every finitely generated submodule $M$ containing $θ(z)−\varphi(w)$ is Hilbert-Schmidt, where $θ(z),$ $\varphi(w)$ are two finite Blaschke products.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2022-0034},
url = {https://global-sci.com/article/81463/hilbert-schmidtness-of-submodules-in-h2-mathbbd2-containing-thzvarphi-w}
}