Vanishing mean oscillation

Summary

A function has vanishing mean oscillation if it has bounded mean oscillation and its mean oscillation over cubes tends to zero as the cubes shrink. The space VMO plays, inside BMO, the role that continuous functions play inside bounded functions. It contains all uniformly continuous functions in BMO, and also some unbounded functions. It was introduced by Sarason, and it appears in the theory of Toeplitz and Hankel operators, of commutators, and of elliptic equations with discontinuous coefficients.