Uniform estimates for the canonical solution to the ∂-equation on product domains

2020/06/25 by Robert Xin Dong, Yifei Pan, Dong, Robert Xin +3
Mathematics · #32W05 #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Primary 32A25 #Secondary 32A26

paper · pdf · doi:10.48550/arxiv.2006.14484

openalex publication_date 2020/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain uniform estimates for the canonical solution to ∂ u=f on the Cartesian product of bounded planar domains with C² boundaries, when f is continuous up to the boundary. This generalizes Landucci's result for the bidisc toward higher dimensional product domains. In particular, it answers an open question of Kerzman for continuous datum.

Related

• Uniform estimates of the Cauchy-Riemann equation on product domains
• Sobolev regularity of the canonical solutions to ∂ on product domains
• Optimal Hölder Regularity of Solution Operator to the ∂-equation on Product Domains
• Solving the Kerzman's problem on the sup-norm estimate for ∂ on product domains
• Product domains, Multi-Cauchy transforms, and the ∂ equation