Hölder and \(L^p\) estimates for \(\square_b\) on CR manifolds of arbitrary codimension

DOI10.1007/s00208-004-0583-5zbMath1076.32030OpenAlexW2095188979MaRDI QIDQ1772071

Mei-Chi Shaw, Lihe Wang

Publication date: 15 April 2005

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

Full work available at URL: https://doi.org/10.1007/s00208-004-0583-5

zbMATH Keywords

Campanato spacesCauchy-Riemann manifolds

Mathematics Subject Classification ID

Analysis on CR manifolds (32V20) Subelliptic equations (35H20) Overdetermined problems for partial differential equations and systems of partial differential equations (35N99)

Related Items

Hölder estimates for subelliptic operators ⋮ Interior \(C^{1,\alpha}\) regularity of weak solutions for a class of quasilinear elliptic equations ⋮ Gradient regularity for elliptic equations in the Heisenberg group ⋮ Boundary Hölder and $L^p$ estimates for local solutions of the tangential Cauchy-Riemann equation ⋮ The \(\bar\partial\)-Cauchy problem and nonexistence of Lipschitz Levi-flat hypersurfaces in \(\mathbb{C}P^n\) with \(n \geq 3\) ⋮ Poincaré lemma and global homotopy formulas with sharp anisotropic Hölder estimates in \(q\)-concave CR manifolds ⋮ Certain Contributions to the $$\bar {\partial }$$ -Problem ⋮ Szegő kernel asymptotics and Morse inequalities on CR manifolds ⋮ MaximalL²and Pointwise Hölder Estimates for □_bonCRManifolds of ClassC² ⋮ Global regularity for the \(\overline{\partial}_b\)-equation on \(C R\) manifolds of arbitrary codimension ⋮ Local solvability in top degree of the semilinear Kohn equation ⋮ \(L^p\)-theory and Serre duality for the tangential Cauchy-Riemann equation ⋮ Local solvability for \(\square_b\) on degenerate CR manifolds and related systems ⋮ Stability of the embeddability under perturbations of the CR structure for compact CR manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Interior a priori estimates for solutions of fully nonlinear equations
• Hypoellipticity of a system of complex vector fields
• Balls and metrics defined by vector fields. I: Basic properties
• Hölder estimates on domains of complex dimension two and on three- dimensional CR manifolds
• The Cauchy kernel, the Szegö kernel, and the Riemann mapping function
• Geometric Lipschitz spaces and applications to complex function theory and nilpotent groups
• Lipschitz functions on spaces of homogeneous type
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Hypoelliptic differential operators and nilpotent groups
• Hölder estimates on CR manifolds with a diagonalizable Levi form
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• The Bergman kernel and biholomorphic mappings of pseudoconvex domains
• Equazioni ellittiche del II\(^ \circ\) ordine e spazi \({\mathcal L}^{(2,\lambda)}\)
• Hypoelliptic second order differential equations
• \(L^ 2\) estimates and existence theorems for the \(\partial\)-operator
• On the extension of holomorphic functions from the boundary of a complex manifold
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• Lectures on Pseudo-Differential Operators: Regularity Theorems and Applications to Non-Elliptic Problems. (MN-24)
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• On the regularity theory of fully nonlinear parabolic equations: II
• Calculus on Heisenberg Manifolds. (AM-119)
• Estimates for the \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \partial \limits^ - _b $\end{document} complex and analysis on the heisenberg group
• Hypoelliptic operators with double characteristics and related pseudo-differential operators
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Schauder and L^PEstimates for Parabolic systems via campanato spaces
• Non‐coercive boundary value problems
• The Neumann Problem for the Cauchy-Riemann Complex. (AM-75)
• A fundamental solution for a subelliptic operator
• The Identity of Weak and Strong Extensions of Differential Operators
• Weak and strong extensions of differential operators

This page was built for publication: Hölder and \(L^p\) estimates for \(\square_b\) on CR manifolds of arbitrary codimension