Estimates for a class of integral operators and applications to the \({\bar\partial}\)-Neumann-problem

DOI10.1007/BF01389097zbMath0569.32008OpenAlexW1966183015MaRDI QIDQ1061277

Ingo Lieb, R. Michael Range

Publication date: 1986

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143375

zbMATH Keywords

strictly pseudoconvex domain\(\partial \)-bar-Neumann-problemintegral representation of forms

Mathematics Subject Classification ID

Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) Linear operators on function spaces (general) (47B38) (overlinepartial) and (overlinepartial)-Neumann operators (32W05) Pseudoconvex domains (32T99)

Related Items

\(L^ p\) and Lipschitz estimates for the \({\bar\partial}\)-equation and the \({\bar\partial}\)-Neumann problem ⋮ The kernel of the \({\bar \partial}\)-Neumann operator on strictly pseudoconvex domains ⋮ Hölder estimates on domains of complex dimension two and on three- dimensional CR manifolds ⋮ Estimations limites pour la solution canonique de l'équation \({\bar \partial}u=f\). (Limit estimates for the canonical solution of the equation \({\bar \partial}u=f)\) ⋮ Hölder estimates for homotopy operators on strictly pseudoconvex domains with \(C^2\) boundary ⋮ Estimates on kernels for the \({\bar \partial}\)-equation and the \({\bar \partial}\)-Neumann problem ⋮ Uniform estimates for the Cauchy-Riemann equation on \(q\)-convex wedges ⋮ The Bergman projection and weighted $C^{k}$ estimates for the canonical solution to the $\bar{\partial}$ problem on non-smooth domains ⋮ Levi metrics and the Romanov-Henkin kernel ⋮ Holomorphic curves in complex spaces ⋮ An asymptotic formula for the Bergman projection on a certain class of domains in \({\mathbb{C}}\) ⋮ Extension of \(A^ t\)-jets from holomorphic submanifolds ⋮ A local Martinelli-Bochner formula on hypersurfaces

Cites Work

• Unnamed Item
• Integral representations and estimates in the theory of the \({\bar\partial}\)-Neumann problem
• Hölderabschätzungen für Ableitungen von Lösungen der Gleichung \(\bar \partial u = f\) bei streng pseudokonvexem Rand
• Estimates for the Bergman and Szegö projections on strongly pseudo-convex domains
• Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudokonvexen Gebieten. Beschränkte Lösungen
• The Hölder continuity of the Bergman projection and proper holomorphic mappings
• Singular integrals related to the Radon transform and boundary value problems
• Holomorphic Lipschitz Functions in Pseudoconvex Domains
• On integral representations for the Neumann operator
• Hölder and L^p estimates for solutions of ∂u = f in strongly pseudoconvex domains
• The Neumann Problem for the Cauchy-Riemann Complex. (AM-75)

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