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- Title
Regularity of the p-Bergman kernel.
- Authors
Chen, Bo-Yong; Xiong, Yuanpu
- 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 < p < 2 is provided. Under the condition that the hyperconvexity index of Ω is positive, we obtain the log-Lipschitz continuity of p ↦ K p (z) for 1 ≤ p ≤ 2 .
- Subjects
LIPSCHITZ continuity; PSEUDOCONVEX domains
- Publication
Calculus of Variations & Partial Differential Equations, 2024, Vol 63, Issue 2, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-023-02643-y