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A property of holomorphic functions related to plurisubharmonic functions (2311.12296v5)
Published 21 Nov 2023 in math.CV and math.FA
Abstract: Let $\varphi $ be a negative plurisubharmonic function in a pseudoconvex domain $\Omega$ in $\mathbb{C}{n}$ and $f$ be a bounded holomorphic function belonging to $L{2}(\Omega, \varphi)$. For all negative plurisubharmonic functions $\psi$ satisfying that $\psi$ is close to $\varphi$ in the $L1(\Omega)$ norm. Using the recent results about $L2-$estimate for $\overline{\partial}-$equation and strong openness conjecture, we prove that there exists a holomorphic function $g$ belonging to $L{2}( \Omega, \psi)$ such that $g$ is close to $f$ in the $L2$ norm on some relatively compact open subset $\Omega{'}$ of $\Omega.$