Integral formulas for the \(\partial\overline\partial\)-equation and zeros of bounded holomorphic functions in the unit ball

DOI10.1007/BF01351413zbMath0414.31007MaRDI QIDQ599219

Bo Berndtsson

Publication date: 1980

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/163399

zbMATH Keywords

areabounded holomorphic functionzero setintegral formulas

Mathematics Subject Classification ID

Axiomatic potential theory (31D05) Holomorphic functions of several complex variables (32A10)

Related Items

Hardy classes and related spaces of analytic functions in the unit circle, polydisc, and the ball ⋮ Weighted -integral representations of smooth functions in the unit ball ofCⁿ ⋮ Zero sets of holomorphic functions in the unit ball with slow growth ⋮ The ends of discs ⋮ Formules explicites pour les solutions minimales de l'équation \(\overline\partial u=f\) dans la boule et dans le polydisque de \(\mathbb C^n\) ⋮ Weighted \(\overline{\partial}\)-integral representations of \(C^1\)-functions in \(\mathbb C^n\) ⋮ Henkin-Ramirez kernels with weight factors ⋮ A properly embedded holomorphic disc in the ball with finite area and dense boundary ⋮ Zeros of bounded holomorphic functions in strictly pseudoconvex domains in \(\mathbb{C}^ 2\) ⋮ The corona problem with two pieces of data ⋮ Ends of varieties ⋮ Canonical homotopy operators for the $\overline{\partial}$ complex in strictly pseudoconvex domains

Cites Work

• Valeurs au bord pour les solutions de l'opérateur $d^n$, et caractérisation des zéros des fonctions de la classe de Nevanlinna
• The Neumann Problem for the Cauchy-Riemann Complex. (AM-75)
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