EXTENSION-THEOREMS FOR FUNCTIONS OF VANISHING MEAN-OSCILLATION

A locally integrable function is said to be of vanishing mean oscillation (VMO) if its mean oscillation over cubes in Rd 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. © 1990 by Pacific Journal of Mathematics.