\(C^{k}\)-estimates for the \(\bar\partial\)-equation on convex domains of finite type

DOI10.1007/s00209-005-0812-yzbMath1114.32005OpenAlexW2149450333MaRDI QIDQ818572

William Alexandre

Publication date: 21 March 2006

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

Full work available at URL: http://www.numdam.org/item?id=AFST_2006_6_15_3_399_0

zbMATH Keywords

convex domainfinite typeCauchy-Riemann equation\(C^k\)-estimates

Mathematics Subject Classification ID

Analytical consequences of geometric convexity (vanishing theorems, etc.) (32F32) Finite-type conditions for the boundary of a domain (32F18)

Related Items

\(C^k\)-estimates for \(\bar{\partial}\)-equation on certain convex domains of infinite type in \(\mathbb{C}^n\) ⋮ Zero sets of \(\mathcal H^p\) functions in convex domains of finite type ⋮ Hölder estimates for homotopy operators on strictly pseudoconvex domains with \(C^2\) boundary ⋮ A solution operator for the \overline∂ equation in Sobolev spaces of negative index ⋮ Estimates for solutions of the \(\bar\partial\)-equation and application to the characterization of the zero varieties of the functions of the Nevanlinna class for lineally convex domains of finite type ⋮ A Berndtsson-Andersson operator solving \({\overline{\partial}}\)-equation with \(W ^{\alpha }\)-estimates on convex domains of finite type ⋮ Weighted Sobolev \(L^p\) estimates for homotopy operators on strictly pseudoconvex domains with \(C^2\) boundary ⋮ \(C^k\)-regularity for \(\bar{\partial}\)-equations for a class of convex domains of infinite type in \(\mathbb{C}^2 \)

Cites Work

• Unnamed Item
• Zero varieties for the Nevanlinna class in convex domains of finite type in \(\mathbb{C}^n\)
• Lösungsoperatoren für den Cauchy-Riemann-Komplex mit \(\mathcal C^K\)- Abschätzungen
• Support functions for convex domains of finite type
• Hölder estimates on convex domains of finite type
• Estimates on the Bergman kernels of convex domains
• Convex domains of finite type
• Randregularität des \({\bar \partial}\)-Problem für stückweise streng pseudokonvexe Gebiete in \({\mathbb C}^ n\). (Boundary regularity of the \({\bar \partial}\)-problem for piecewise strongly pseudoconvex domains in \({\mathbb C}^ n)\)
• Zero varieties for the Nevanlinna class on all convex domains of finite type
• Extension of C ∞ Functions Defined in a Half Space
• \(L^p\) estimates on convex domains of finite type

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