We introduce a new decreasing rearrangement for functions defined on a homogeneous tree,
which enjoys very intuitive and natural properties. The idea is to iterate, with respect to a particular
ordering, the usual one dimensional rearrangement on each geodesic. After showing the canonicity
of this definition and the axioms of ...»»»»
We introduce a new decreasing rearrangement for functions defined on a homogeneous tree,
which enjoys very intuitive and natural properties. The idea is to iterate, with respect to a particular
ordering, the usual one dimensional rearrangement on each geodesic. After showing the canonicity
of this definition and the axioms of symmetrization, we prove our main result: the geometric and
analytic definitions, in terms of the “layer cake” formula, agree.^^^^