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arXiv · 0709.0648

Rearrangement transformations on general measure spaces

Santiago Boza·Javier Soria
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Abstract

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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Santiago Boza, Javier Soria. 2007-09-05. Rearrangement transformations on general measure spaces. https://arxiv.org/abs/0709.0648

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