Postorder rearrangement operators

Abstract

We investigate the rearrangement of the Haar system induced by the postorder on the set of dyadic intervals in $[0,1]$ with length greater than or equal to $2^{-N}$. By means of operator norms on ${\text{BMO}}_N$ we prove that the postorder has maximal distance to the usual lexicographic order.

21 pages, To appear in Quarterly Journ. Math