Integral solution operators for the Cauchy-Riemann equations on pseudoconvex domains

DOI10.1007/BF01453566zbMath0698.47020OpenAlexW1997388349MaRDI QIDQ912370

N. E. Zubov

Publication date: 1990

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

Full work available at URL: https://eudml.org/doc/164628

zbMATH Keywords

pseudoconvex domaind-bar-equation

Mathematics Subject Classification ID

Linear operators on function spaces (general) (47B38) Pseudoconvex domains (32T99)

Related Items

On the extension of \(L^ 2\) holomorphic functions. III: Negligible weights ⋮ The explicit solutions of \(C_{p,q}^{k+\alpha}\)-form for the \(\overline{\partial}\)-equations on pseudoconvex open sets ⋮ Extension of holomorphic L²-functions with weighted growth conditions ⋮ Sobolev embedding in \(\mathbb{C}^ n\) and the \(\bar \partial\)-equation ⋮ On the extension of L² holomorphic functions V-Effects of generalization ⋮ Hölder and \(L^ p\)-estimates for the \(\bar\partial\)-equation on non- smooth strictly \(q\)-convex domains ⋮ On Hölder and BMO estimates for \(\overline \partial\) on convex domains in \(\mathbb{C}^ 2\) ⋮ Solving withL^p-estimates onq-convex intersections in complex manifold ⋮ The \(\bar{\partial}\)-equation on an annulus between two strictly \(q\)-convex domains with smooth boundaries ⋮ On the parameter dependence of solutions to the \(\bar\partial\)-equation ⋮ Unnamed Item ⋮ Estimates for the \({\bar \partial}\)-equation and zeros of holomorphic functions on the Lie-ball ⋮ A smooth pseudoconvex domain in \(\mathbb C^ 2\) for which \(L^ \infty\)- estimates for \(\overline\partial\) do not hold

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the extension of \(L^ 2\) holomorphic functions
• Boundary behavior of the Bergman kernel function on pseudoconvex domains
• The Bergman kernel on uniformly extendable pseudoconvex domains
• Sup-norm estimates for \({\bar\partial}\) in \({\mathbb{C}}^ 2\)
• Sharp Hölder estimates for \({\bar\partial}\) on ellipsoids
• Hölder estimates on domains of complex dimension two and on three- dimensional CR manifolds
• Henkin-Ramirez kernels with weight factors
• Solutions de l'équation \(\bar\partial\) et zéros de la classe de Nevanlinna dans certains domaines faiblement pseudo-convexes
• Peak points on weakly pseudoconvex domains
• Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions
• Lokale Kerne und beschränkte Lösungen für den \(\bar\partial\)-Operator auf \(q\)-konvexen Gebieten
• Carleman estimates for the Laplace-Beltrami equation on complex manifolds
• Ein Divisionsproblem und Randintegraldarstellungen in der komplexen Analysis
• Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudokonvexen Gebieten. Beschränkte Lösungen
• A pseudo-convex domain not admitting a holomorphic support function
• L^∞-continuity of Henkin operators solving in certain weakly pseudoconvex domains of ℂ²
• L'équation $\overline \partial $ dans certains domaines faiblement convexes
• Estimates for the ∂̄-Neumann problem for pseudoconvex domains in C ² of finite type
• Regularity Properties of the ∂ b Equation on Weakly Pseudoconvex CR Manifolds of Dimension 3
• Extension of holomorphic L²-functions with weighted growth conditions
• INTEGRAL REPRESENTATION OF FUNCTIONS IN STRICTLY PSEUDOCONVEX DOMAINS AND APPLICATIONS TO THE $ \overline{\partial}$-PROBLEM
• Hölder and L^p estimates for solutions of ∂u = f in strongly pseudoconvex domains
• Integral Representation Formulas and $L^p$-Estimates for the $\bar{\partial}$-Equation.