Monotone rearrangement does not increase generalized Campanato norm in VMO

Abstract

We consider a quantitative version of the space VMO on an interval, equipped with a quadratic Campanato-type norm, and prove that monotone rearrangement does not increase the norm in this space.

15 pages, 6 figures. In this version, the main theorem (Th. 1.3) is strengthened to omit the previous requirement of admissibility of ξ