Journal of Operator Theory

Volume 83, Issue 2, Spring 2020  pp. 333-352.

Essential normality of principal submodules of the Hardy module on a strongly pseudo-convex domain

Authors:  Yi Wang (1), Jingbo Xia (2)
Author institution:(1) Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260, U.S.A.
(2) Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260, U.S.A.

Summary: Let $\Omega$ be a bounded, strongly pseudo-convex domain with smooth boundary in $\mathbb{C}^n$. Suppose that $h$ is an analytic function defined on an open set containing $\overline{\Omega }$. We show that the principal submodule of the Hardy module $H^2(\Omega )$ generated by $h$ is $p$-essentially normal for $p > n$.

DOI: http://dx.doi.org/10.7900/jot.2018oct09.2224
Keywords: strongly pseudo-convex domain, essential normality, Hardy module, submodule