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arXiv · 2201.05130

Vanishing Mean Oscillation and Continuity of Rearrangements

Almut Burchard·Galia Dafni·Ryan Gibara
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Abstract

We study the decreasing rearrangement of functions in VMO, and show that for rearrangeable functions, the mapping f -> f* preserves vanishing mean oscillation. Moreover, as a map on BMO, while bounded, it is not continuous, but continuity holds at points in VMO (under certain conditions). This also applies to the symmetric decreasing rearrangement. Many examples are included to illustrate the results.

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Almut Burchard, Galia Dafni, Ryan Gibara. 2022-01-13. Vanishing Mean Oscillation and Continuity of Rearrangements. https://arxiv.org/abs/2201.05130

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