The Helmholtz Decomposition of a BMO Type Vector Field in a Slightly Perturbed Half Space

Abstract

We introduce a space of L^2 vector fields with bounded mean oscillation whose “normal” component to the boundary is well-controlled. We establish its Helmholtz decomposition in the case when the domain is a perturbed C^3 half space in {textbf{R}}^n(n ge 3) with small perturbation.