Acta Mathematica Vietnamica | 2019
On Hölder Estimates with Loss of Order One for the ∂̄$\\bar {\\partial }$ Equation on a Class of Convex Domains of Infinite Type in ℂ3$\\mathbb {C}^{3}$
Abstract
AbstractIn this paper, we establish a Hölder continuity with loss of order one for the Cauchy-Riemann equation on a class of smoothly bounded, convex domains of infinite type in the sense of Range in ℂ3$\\mathbb {C}^{3}$. Let Ω be such a domain and let φ be a (0,1)-form defined continuously on Ω̄$\\bar {\\Omega }$. Then, if φ is Lipschitz continuity on bΩ, in the sense of distributions, there exists a function u belonging to a “suitable” Hölder class such that \n∂̄u=φin Ω.$$\\bar{\\partial} u=\\varphi \\quad \\text{ in } {\\Omega}. $$