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
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