On Sharp Hölder Estimates of the Cauchy-Riemann Equation on Pseudoconvex Domains in Cn with One Degenerate Eigenvalue

Abstract

Let Ω be a smoothly bounded pseudoconvex domain in Cn with one degenerate eigenvalue and assume that there is a smooth holomorphic curve V whose order of contact with bΩ at z0∈bΩ is larger than or equal to η. We show that the maximal gain in Hölder regularity for solutions of the ∂¯-equation is at most 1/η.