Sobolev embedding in \(\mathbb{C}^ n\) and the \(\bar \partial\)-equation

DOI10.1007/BF02921308zbMath0743.32015MaRDI QIDQ1177611

Aline Bonami, Nessim Sibony

Publication date: 26 June 1992

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

zbMATH Keywords

Sobolev embedding\(\overline\partial\)-equation

Mathematics Subject Classification ID

(overlinepartial) and (overlinepartial)-Neumann operators (32W05) Pseudoconvex domains (32T99)

Related Items

L^p mapping properties for the Cauchy–Riemann equations on Lipschitz domains admitting subelliptic estimates ⋮ Duality of the Bergman spaces on some weakly pseudoconvex domains ⋮ On compactness and Lp‐regularity in the ∂¯‐Neumann problem ⋮ Sobolev inequalities and the \(\overline{\partial }\)-Neumann operator

Cites Work

• Integral solution operators for the Cauchy-Riemann equations on pseudoconvex domains
• \(L^ 2\) estimates and existence theorems for the tangential Cauchy-Riemann complex
• \(L^ p\) and Lipschitz estimates for the \({\bar\partial}\)-equation and the \({\bar\partial}\)-Neumann problem
• The range of the tangential Cauchy-Riemann operator
• Analysis on the Heisenberg group and estimates for functions in Hardy classes of several complex variables
• Construction of p.s.h. functions on weakly pseudoconvex domains
• Boundary behavior of functions holomorphic in domains of finite type
• Boundary Regularity for Harmonic Hardy-Sobolev Spaces
• Estimates for the ∂̄-Neumann problem for pseudoconvex domains in C ² of finite type
• Global Regularity for $\overline \partial$ on Weakly Pseudo-Convex Manifolds
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