Uniform estimates with weights for the \(\overline{\partial}\)-equation

DOI10.1007/BF02921720zbMath0923.32014MaRDI QIDQ1272836

Bo Berndtsson

Publication date: 6 October 1999

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

zbMATH Keywords

corona problem\(L^2\) estimates\(d\)-bar equation

Mathematics Subject Classification ID

(overlinepartial) and (overlinepartial)-Neumann operators (32W05) (H^p)-spaces, Nevanlinna spaces of functions in several complex variables (32A35)

Related Items

A \(L^2\) estimate for the minimal solution of \(\overline{\partial}\) on the unit ball ⋮ Parameter dependence of the Bergman kernels ⋮ The logarithm of the modulus of a holomorphic function as a minorant for a subharmonic function ⋮ Geometric conditions for multiple sampling and interpolation in the Fock space ⋮ Sharp pointwise and uniform estimates for \(\bar{\partial} \) ⋮ Toeplitz operators and Carleson measures on generalized Bargmann-Fock spaces ⋮ Asymptotic normality of linear statistics of zeros of random polynomials ⋮ Integral formulas and the Ohsawa-Takegoshi extension theorem ⋮ Sampling in weighted \(L^p\) spaces of entire functions in \(\mathbb{C}^n\) and estimates of the Bergman kernel ⋮ Interpolation and sampling hypersurfaces for the Bargmann-Fock space in higher dimensions ⋮ The extension theorem of Ohsawa-Takegoshi and the theorem of Donnelly-Fefferman ⋮ Pointwise estimates for the weighted Bergman projection kernel in \({\mathbb C}^n\), using a weighted \(L^2\) estimate for the \(\bar\partial\) equation ⋮ Optimal polynomial prediction measures and extremal polynomial growth

Cites Work

• Problème de la couronne pour des domaines pseudoconvexes à bord lisse. (The current problem for pseudoconvex domains with smooth boundary)
• Wolff's proof of the corona theorem
• On the \(\bar {\partial{}}\) equation in weighted \(L^ 2\) norms in \(\mathbb{C} ^ 1\)
• Weighted estimates for \(\overline\partial\) in domains in \(\mathbb{C}\)
• Prolongement des fonctions holomorphes bornees et métrique de Caratheodory
• BMO functions and the \(\overline\partial\)-equation
• A smooth pseudoconvex domain in \(\mathbb C^ 2\) for which \(L^ \infty\)- estimates for \(\overline\partial\) do not hold
• \(H^ p\)-estimates of holomorphic division formulas
• \(\overline\partial\) and Schrödinger operators
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• Interpolations by bounded analytic functions and the corona problem
• Generators for some rings of analytic functions
• The Neumann Problem for the Cauchy-Riemann Complex. (AM-75)
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