A \(L^2\) estimate for the minimal solution of \(\overline{\partial}\) on the unit ball

DOI10.1016/j.jmaa.2022.126136zbMath1487.32200OpenAlexW4214824208MaRDI QIDQ831500

Phung Trong Thuc

Publication date: 23 March 2022

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2022.126136

zbMATH Keywords

Bergman metric\(L^2\) estimates\(\overline{\partial}\) equationweighted Bergman kernels

Mathematics Subject Classification ID

(overlinepartial) and (overlinepartial)-Neumann operators (32W05) Bergman spaces of functions in several complex variables (32A36)

Cites Work

• Weighted Bergman projections on the Hartogs triangle: exponential decay
• On the extension of \(L^ 2\) holomorphic functions
• \(L^ 2\)-cohomology and index theorem for the Bergman metric
• Weights of holomorphic extension and restriction
• Uniform estimates with weights for the \(\overline{\partial}\)-equation
• The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman
• Compactness of the \(\overline{\partial} \)-Neumann problem on domains with bounded intrinsic geometry
• New estimates for the minimal \(L^{2}\) solution of \(\bar{\partial}\) and applications to geometric function theory in weighted Bergman spaces
• Bergman kernel and hyperconvexity index
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• A Comparison Principle for Bergman Kernels
• A note on the Hörmander, Donnelly-Fefferman, and Berndtsson L²-estimates for the ∂-operator

This page was built for publication: A \(L^2\) estimate for the minimal solution of \(\overline{\partial}\) on the unit ball