Subelliptic and Maximal L^p Estimates for the Complex Green Operator on non-pseudoconvex domains

2025/04/14 by Joel Coacalle, Coacalle, Joel
Mathematics · #32V35 #35A27 #35B65 #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Primary: 32W10 #Secondary: 32F17

paper · pdf · doi:10.48550/arxiv.2504.10614

openalex publication_date 2025/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove subelliptic estimates for ethe complex Green operator K_q at a specific level q of the ∂_b -complex, defined on a not necessarily pseudoconvex CR manifold satisfying the commutator finite type condition. Additionally, we obtain maximal L^p estimates for K_q by considering closed-range estimates. Our results apply to a family of manifolds that includes a class of weak Y(q) manifolds satisfying the condition D(q) . We employ a microlocal decomposition and Calderón-Zygmund theory to obtain subelliptic and maximal- L^p estimates, respectively.

Related

• Superlogarithmic estimates on pseudoconvex domains and CR manifolds
• L²-Sobolev theory for the complex Green operator
• L^p-L^q estimates for subelliptic pseudo-differential operators on compact Lie groups
• Closed range estimates for ∂_b on CR manifolds of hypersurface type
• Sobolev estimates for the complex Green operator on CR submanifolds of hypersurface type