Product domains, multi-Cauchy transforms, and the \(\bar{\partial}\) equation

DOI10.1016/j.aim.2019.106930zbMath1439.32097arXiv1904.09401OpenAlexW2990128931MaRDI QIDQ2281342

Yanyan Li

Publication date: 19 December 2019

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.09401

zbMATH Keywords

Cauchy-Riemann equationsintegral solution operators

Mathematics Subject Classification ID

Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels) (32A26) (overlinepartial) and (overlinepartial)-Neumann operators (32W05)

Related Items

A survey of the \(L^p\) regularity of the Bergman projection ⋮ Optimal Hölder regularity for the ∂̄ problem on product domains in ℂ² ⋮ Some estimates for the Cauchy transform in higher dimensions ⋮ Sobolev regularity of the canonical solutions to \(\bar{\partial}\) on product domains ⋮ Sharp pointwise and uniform estimates for \(\bar{\partial} \) ⋮ On the canonical solution of \(\overline{\partial}\) on polydisks ⋮ Hölder estimates for the ∂̄ problem for (p,q) forms on product domains

Cites Work

• The Cauchy-Riemann equations on product domains
• On supnorm estimates for \(\bar \partial\) on infinite type convex domains in \(\mathbb C^{2}\)
• \(L^\infty\) estimates for the \(\bar\partial\) problem in a half-plane
• Sup-norm estimates for \({\bar\partial}\) in \({\mathbb{C}}^ 2\)
• Biholomorphic mappings and the \(\overline\partial\)-problem
• Wolff's proof of the corona theorem
• Optimal Lipschitz and \(L^p\) regularity for the equation \(\overline\partial u=f\) on strongly pseudo-convex domains
• A simplification and extension of Fefferman's theorem on biholomorphic mappings
• Duality and approximation of Bergman spaces
• Lectures on the \(L^2\)-Sobolev theory of the \(\bar\partial\)-Neumann problem
• \(L^2\) extension of \(\overline{\partial}\)-closed forms from a hypersurface
• Die Cauchy-Riemannschen Differentialgleichungen auf streng pseudokonvexen Gebieten. Beschränkte Lösungen
• Uniform estimates for the \(\bar\partial\)-equation on domains with piecewise smooth strictly pseudoconvex boundaries
• Cauchy-type integrals in several complex variables
• The $\overline {\partial }$ problem on domains with piecewise smooth boundaries with applications
• Global Regularity for $\overline \partial$ on Weakly Pseudo-Convex Manifolds
• Hölder and L^p estimates for solutions of ∂u = f in strongly pseudoconvex domains
• Integral Representation Formulas and $L^p$-Estimates for the $\bar{\partial}$-Equation.
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