Regularity of the p-Bergman kernel

2023/02/14 by Chen, Bo-Yong, Xiong, Yuanpu · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.06877

Abstract

We show that the p-Bergman kernel K_p(z) on a bounded domain Ω is of locally C^1,1 for p≥1.The proof is based on the locally Lipschitz continuity of the off-diagonal p-Bergman kernel K_p(ζ,z) for fixed ζ∈ Ω. Global irregularity of K_p(ζ,z) is presented for some smooth strongly pseudoconvex domains when p≫ 1. As an application of the local C^1,1-regularity, an upper estimate for the Levi form of log K_p(z) for 1

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• On the p-Bergman kernel with respect to a functional ξ

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