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On smoothing of plurisubharmonic functions on unbounded domains (2104.14448v1)
Published 29 Apr 2021 in math.CV
Abstract: We prove that for every $n \ge 2$, there exists a pseudoconvex domain $\Omega \subset \mathbb{C}n$ such that $\mathfrak{c}0(\Omega) \subsetneq \mathfrak{c}1(\Omega)$, where $\mathfrak{c}k(\Omega)$ denotes the core of $\Omega$ with respect to $\mathcal{C}k$-smooth plurisubharmonic functions on $\Omega$. Moreover, we show that there exists a bounded continuous plurisubharmonic function on $\Omega$ that is not the pointwise limit of a sequence of $\mathcal{C}1$-smooth bounded plurisubharmonic functions on $\Omega$.