Extension theorems for functions of vanishing mean oscillation (Q1113035)

A locally integrable function is said to be of vanishing mean oscillation (VMO) if its mean oscillation over cubes in \({\mathbb{R}}^ d\) converges to zero with the volume of the cubes. We establish necessary and sufficient conditions for a locally integrable function defined on a bounded measurable set of positive measure to be the restriction to that set of a VMO function.