Rearrangement transformations on general measure spaces

Details Rearrangement transformations on general measure spaces Rearrangement transformations on general measure spaces

2007-09-05

arxiv.org/abs/0709.0648v1

Mathematics

Functional Analysis

17 pages

Scientific paper

For a general set transformation ${\cal R}$ 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 ${\cal R}$, giving a unified approach to the classical rearrangement, Steiner's symmetrization, the multidimensional case, and the discrete setting of trees.

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