On the parameter dependence of solutions to the \(\bar\partial\)-equation

DOI10.1007/BF01446590zbMath0789.35119MaRDI QIDQ1814120

Takeo Ohsawa, Klas Diederich

Publication date: 25 June 1992

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

Full work available at URL: https://eudml.org/doc/164799

zbMATH Keywords

Cauchy-Riemann equations on pseudoconvex domainsintegral solution operatorsregularity in the parameter

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) A priori estimates in context of PDEs (35B45) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) (overlinepartial) and (overlinepartial)-Neumann operators (32W05) (overlinepartial)-Neumann problems and formal complexes in context of PDEs (35N15)

Related Items

Parameter dependence of the Bergman kernels ⋮ The \(\overline{\partial}\)-equation on variable strictly pseudoconvex domains ⋮ Behavior of the Bergman kernel at infinity ⋮ The \({\overline{\partial}}\) operator along the leaves and Guichard's theorem for a complex simple foliation ⋮ Leafwise Dolbeault cohomology of certain complex foliations ⋮ On projectively embeddable complex-foliated structures

Cites Work

• On the extension of \(L^ 2\) holomorphic functions
• Integral kernels and Hölder estimates for \({\bar \partial}\) on pseudoconvex domains of finite type in \({\mathbb{C}}^ 2\)
• Integral solution operators for the Cauchy-Riemann equations on pseudoconvex domains
• The Bergman kernel on uniformly extendable pseudoconvex domains
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• Extension of holomorphic L²-functions with weighted growth conditions
• Application des techniques $L^2$ à la théorie des idéaux d'une algèbre de fonctions holomorphes avec poids

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