Author

Hong-Rong Chen

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Preprint Sep 2026

Energy asymptotics of holomorphic functions with application to Calder\'{o}n-Zygmund theory in $\mathbb{C}$

The Calder\'on-Zygmund theory establishes the boundedness of singular integral operators on $L^p$ spaces for $1<p<\infty$, yet it encounters a failure at the endpoint $p = 1$. While radial counterexamples in $\mathbb{R}^n$ are well-documented, Pan-Shao-Wang-Wu \cite{psww2026} has showed that every nonconstant holomorph...

Hong-Rong Chen, Guo-Kuan Shao, Ju-Jie Wu et al. · 0 citations

Preprint Sep 2026

Characterization of Sobolev regularity of plurisubharmonic functions

Let $f$ be a nonzero holomorphic germ at $0 \in \mathbb C^n$ with $f(0)=0$, and let $\chi$ be a $C^2$ non-decreasing convex function on the left half-line. We establish sharp necessary and sufficient conditions for the local Sobolev regularity of the plurisubharmonic function $v=\chi(\log|f|).$ The criteria for the $L^...

Hong-Rong Chen, Guo-Kuan Shao, Wen-Xuan Wang · 0 citations