On supnorm estimates for ∂ on infinite type convex domains in \mathbb C²

2009/11/12 by John Erik Fornæss, John Erik Fornaess, Lina Lee +4
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.CV

paper · pdf · doi:10.48550/arxiv.0911.2277

15 pages. submitted to J. Geom. Anal

arxiv created 2009/11/12 · openalex publication_date 2009/11/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the ∂-equation on some convex domains of infinite type in \mathbb C². In detail, we prove that supnorm estimates hold for infinite exponential type domains provided the exponent is less than 1.

Related

• Supnorm estimates for ∂ on product domains in ℂⁿ
• A berndtsson-Andersson operator solving ∂-equation with W^α-estimates on convex domains of finite type
• Weighted estimates for solutions of the ∂ -equation for lineally convex domains of finite type and applications to weighted bergman projections
• Zero sets of functions in the Nevanlinna class and the ∂_b-equation on convex domains of general type in ℂ²
• Solving the Kerzman's problem on the sup-norm estimate for ∂ on product domains