Rearrangement transformations on general measure spaces

Abstract

For a general set transformation $\mathcal{R}$ between two measure spaces, we define the rearrangement of a measurable function by means of the Layer's cake formula. We study some functional properties of the Lorentz spaces defined in terms of $\mathcal{R}$, giving a unified approach to the classical rearrangement, Steiner's symmetrization, the multidimensional case, and the discrete setting of trees.

17 pages