Extension theorem for $bmo$ in a domain

Abstract

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.