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Acta Mathematica Vietnamica

On Hölder Estimates with Loss of Order One for the ¯ Equation on a Class of Convex Domains of Infinite Type in C3

icon-email Ly Kim Ha

Abstract

In 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. Let Ω be such a domain and let φ be a (0,1)-form defined continuously on Ω¯. 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 ¯u=φ in Ω.