An inequality of rearrangements on the unit circle

@inproceedings{Draghici2007AnIO,
  title={An inequality of rearrangements on the unit circle},
  author={Cristina Draghici},
  year={2007}
}
We prove that the integral of the product of two functions over a symmetric set in $\mathbb{S}^1\times\mathbb{S}^1$ , defined as $E=\{(x,y)\in\mathbb{S}^1\times\mathbb{S}^1:d(\sigma_1(x),\sigma_2(y))\leq\alpha\}$ (where $\sigma_1$ , $\sigma_2$ are diffeomorphisms of $\mathbb{S}^1$ with certain properties and $d$ is the geodesic distance on $\mathbb{S}^1$ ), increases when we pass to their symmetric decreasing rearrangement. We also give a characterization of the diffeomorphisms $\sigma_1… CONTINUE READING

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