Sobolev estimates for the complex green operator on a class of weakly pseudoconvex boundaries

DOI10.1080/03605309108820813zbMath0747.32007OpenAlexW2010173617WikidataQ57376107 ScholiaQ57376107MaRDI QIDQ3986384

Harold P. Boas, Emil J. Straube

Publication date: 27 June 1992

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309108820813

zbMATH Keywords

tangential Cauchy-Riemann equationsSzegö projectionweakly pseudoconvex boundaries

Mathematics Subject Classification ID

(overlinepartial) and (overlinepartial)-Neumann operators (32W05) Pseudoconvex domains (32T99) (overlinepartial)-Neumann problems and formal complexes in context of PDEs (35N15)

Related Items

On Hardy spaces on worm domains ⋮ The Diederich-Fornaess index and the regularities on the \bar{\partial}-Neumann problem ⋮ A comparison between the Bergman and Szegö kernels of the non-smooth worm domain \(D'_{\beta }\) ⋮ Sharp estimates for the Szegő projection on the distinguished boundary of model worm domains ⋮ Hardy spaces and the Szegő projection of the non-smooth worm domain \(D_\beta^\prime\) ⋮ L2-Sobolev theory for the complex Green operator ⋮ The Kohn-Laplace equation on abstract CR manifolds: Global regularity ⋮ Domains with maximal estimate. ⋮ The complex green operator with Sobolev estimates up to a finite order ⋮ Sobolev estimates for the complex Green operator on CR submanifolds of hypersurface type ⋮ Estimates for the complex Green operator: Symmetry, percolation, and interpolation ⋮ Compactness of the complex Green operator on CR-manifolds of hypersurface type ⋮ The ∂¯-Neumann operator with Sobolev estimates up to a finite order ⋮ The complex Green operator on CR-submanifolds of $\mathbb{C}^{n}$ of hypersurface type: Compactness

Cites Work

• Equivalence of regularity for the Bergman projection and the \({\bar \partial}\)-Neumann operator
• Sobolev estimates for the \({\bar \partial}\)-Neumann operator on domains in \({\mathbb{C}}^ n\) admitting a defining function that is plurisubharmonic on the boundary
• \(L^ 2\) estimates and existence theorems for the tangential Cauchy-Riemann complex
• Sobolev estimates for the Lewy operator on weakly pseudo-convex boundaries
• Estimates for the Bergman and Szegö projections on strongly pseudo-convex domains
• On the global real analyticity of solutions to the neumann problems