A property of holomorphic functions related to plurisubharmonic functions

2023/11/21 by Nguyen Van Phu, Van Phu, Nguyen
Mathematics · #32U05 #32U15 #32W05 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2311.12296

openalex publication_date 2023/11/21 · openalex created_date 2023/11/23 · openalex updated_date 2026/07/28

Abstract

Let φ be a negative plurisubharmonic function in a pseudoconvex domain Ω in ℂⁿ and f be a bounded holomorphic function belonging to L²(Ω, φ). For all negative plurisubharmonic functions ψ satisfying that ψ is close to φ in the L¹(Ω) norm. Using the recent results about L²-estimate for ∂-equation and strong openness conjecture, we prove that there exists a holomorphic function g belonging to L²( Ω, ψ) such that g is close to f in the L² norm on some relatively compact open subset Ω^' of Ω.

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