Hölder and \(L^ p\)-estimates for the \({\bar\partial}\)-equation in some convex domains with real-analytic boundary

DOI10.1007/BF01450763zbMath0533.32010MaRDI QIDQ789578

Joan del Castillo, Joaquim Bruna

Publication date: 1984

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

Full work available at URL: https://eudml.org/doc/163946

zbMATH Keywords

\(\bar\partial\)-equationconvex domainsHölder estimates

Mathematics Subject Classification ID

(overlinepartial) and (overlinepartial)-Neumann operators (32W05) (H^p)-spaces, Nevanlinna spaces of functions in several complex variables (32A35) Geometric convexity in several complex variables (32F99)

Related Items

Hölder estimates on domains of complex dimension two and on three- dimensional CR manifolds ⋮ \(C^k\)-estimates for \(\bar{\partial}\)-equation on certain convex domains of infinite type in \(\mathbb{C}^n\) ⋮ L^p estimates for the $\bar\partial$-equation on a class of infinite type domains ⋮ Tangential Cauchy-Riemann equations on pseudoconvex boundaries of finite and infinite type in \(\mathbb {C}^2\) ⋮ L'équation $\overline \partial $ dans certains domaines faiblement convexes ⋮ Supnorm and \(f\)-Hölder estimates for \(\overline\partial\) on convex domains of general type in \(\mathbb C^2\) ⋮ L^p (1 ≤ p ≤ ∞) estimates for on a certain pseudoconvex domain in ℂⁿ ⋮ On Hölder estimates with loss of order one for the \(\bar{\partial}\) equation on a class of convex domains of infinite type in \(\mathbb {C}^{3}\) ⋮ \( L^p\) and Hölder estimates for Cauchy-Riemann equations on convex domain of finite/infinite type with piecewise smooth boundary in \(\mathbb{C}^2\) ⋮ Sharp Hölder estimates for {̄∂} on ellipsoids and their complements via order of contact ⋮ Unnamed Item ⋮ Hölder and \(L^p\) estimates for the \({\bar{\partial }}\)-equation in a class of convex domains of infinite type in \({\mathbb{C}}^n\) ⋮ \(L^p\) estimates for \(\overline\partial\)-equation on generalized complex ellipsoids ⋮ Optimal \(L^ p\) estimates for the \(\bar \partial\)-equation on complex ellipsoids in \(\mathbb{C}^ n\) ⋮ Hölder estimates for local solutions for \(\overline\partial\) on a class of nonpseudoconvex domains

Cites Work

• Unnamed Item
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• The Szegö kernel in terms of Cauchy-Fantappie kernels
• Ein Divisionsproblem und Randintegraldarstellungen in der komplexen Analysis
• Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudokonvexen Gebieten. Beschränkte Lösungen
• An Elementary Integral Solution Operator for the Cauchy-Riemann Equations on Pseudoconvex Domains in C n
• Singular Points of Complex Hypersurfaces. (AM-61)
• INTEGRAL REPRESENTATION OF FUNCTIONS IN STRICTLY PSEUDOCONVEX DOMAINS AND APPLICATIONS TO THE $ \overline{\partial}$-PROBLEM
• EXACT HÖLDER ESTIMATES FOR THE SOLUTIONS OF THE $ \bar\partial$-EQUATION