Dyadic-BMO functions, the dyadic Gurov-Reshetnyak conditions on $[0,1{]}^n$ and rearrangements of functions

Abstract

We introduce the space of dyadic bounded mean oscillation functions $f$ defined on $[0,1{]}^n$ and study the behavior of the nonincreasing rearrangement of $f$, as an element of the space $BMO((0,1])$. We also study the analogous class of functions that satisfy the dyadic Gurov-Reshetnyak condition and look upon their integrability properties.

15 pages