Existence and regularity theorems for d and ∂ ̄ $\bar{\partial }$ in Hölder–Zygmund spaces on half-spaces

Abstract This paper is devoted to establish existence and regularity theorems for the d - and ∂ ̄ $\bar{\partial }$ -equations in the domains C + n ${\mathbb{C}}_{+}^{n}$ and R + n + 1 ${\mathbb{R}}_{+}^{n+1}$ , respectively, for differential forms in Hölder–Zygmund spaces. Consequently, the same regularity results are obtained for the ∂ ∂ ̄ $\partial \bar{\partial }$ -equation. Our analysis also extends to the case of differential forms admitting boundary values in the sense of currents.