  The $bmo$ space, also known as the local $BMO$ space, is the $BMO$ space
which is uniformly locally $L^1$ in addition. In this article, we establish an
extension theorem for the $bmo$ space defined in an arbitrary uniformly $C^2$
domain. This extension theorem results in a product estimate for $bmo$
functions defined in an arbitrary uniformly $C^2$ domain.
