The cone of rearrangements for generalized Bessel potentials

A space of generalized Bessel potentials constructed on the basis of rearrangement-invariant spaces is considered. An equivalent description of the cone of decreasing rearrangements is proposed for functions from the space of generalized Bessel potentials. An additional characterization of the cone of decreasing rearrangements is obtained in the case of spaces separated from the space L 1. © 2008 MAIK Nauka.