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We consider a space of $L^2$ vector fields with bounded mean oscillationwhose ``normal'' component to the boundary is well-controlled. In the case whenthe dimension $n \geq 3$, we establish its Helmholtz decomposition forarbitrary uniformly $C^3$ domain in $\mathbf{R}^n$.

The Helmholtz decomposition of a $BMO$ type vector field in general unbounded domains