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

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