Weighted estimates for \(\overline\partial\) in domains in \(\mathbb{C}\)

DOI10.1215/S0012-7094-92-06607-5zbMath0774.35048OpenAlexW1499108554MaRDI QIDQ1196386

Bo Berndtsson

Publication date: 14 December 1992

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-92-06607-5

zbMATH Keywords

weighted \(L^ p\)-estimates for the \(\overline\partial\)-equation

Mathematics Subject Classification ID

(overlinepartial) and (overlinepartial)-Neumann operators (32W05) Capacity and harmonic measure in the complex plane (30C85) Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions (31A15) (overlinepartial)-Neumann problems and formal complexes in context of PDEs (35N15)

Related Items (18)

One-parameter families of operators in \(\mathbb C\) ⋮ \(\bar{\partial}\)-equation look at analytic Hilbert's zero-locus theorem ⋮ Hankel operators on the weighted Bergman spaces with exponential type weights ⋮ Cauchy-Riemann \(\bar{\partial}\)-equations with some applications ⋮ Heat equations in \(\mathbb {R} \times \mathbb {C}\) ⋮ Suita conjecture and the Ohsawa-Takegoshi extension theorem ⋮ Multiple sampling and interpolation in Bergman spaces ⋮ Almost holomorphic extensions of ultradifferentiable functions ⋮ On the \(\bar {\partial{}}\) equation in weighted \(L^ 2\) norms in \(\mathbb{C} ^ 1\) ⋮ Uniform estimates in the Poincaré-Aronszajn theorem on the separation of singularities of analytic functions ⋮ The \(\square_b\)-heat equation on quadric manifolds ⋮ \(L^p\)-estimates and existence theorems for the \(\bar \partial\)-operator on complete Kähler manifolds ⋮ Some estimates for the Bergman Kernel and Metric in Terms of Logarithmic Capacity ⋮ A simplified calculation for the fundamental solution to the heat equation on the Heisenberg group ⋮ Some applications of the Ohsawa-Takegoshi extension theorem ⋮ The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman ⋮ Uniform estimates with weights for the \(\overline{\partial}\)-equation ⋮ A smooth pseudoconvex domain in \(\mathbb C^ 2\) for which \(L^ \infty\)- estimates for \(\overline\partial\) do not hold

Cites Work

• \(L^\infty\) estimates for the \(\bar\partial\) problem in a half-plane
• On the \(\bar {\partial{}}\) equation in weighted \(L^ 2\) norms in \(\mathbb{C} ^ 1\)
• Generators for some rings of analytic functions
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