# 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

## Inequalities of Riesz-Sobolev type for compact connected Abelian groups.

• Mathematics
• 2018

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 14 REFERENCES

## II

• A. Baernstein
• Convolution and rearrangement on the circle. Complex Variables Theory Appl., 12(1-4):33–37
• 1989
VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

## Rearrangements of functions

• Mathematics
• 1986
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

## Analysis

• E. H. Lieb, M. Loss
• volume 14 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, second edition
• 2001
VIEW 1 EXCERPT

## A unified approach to symmetrization

• II A. Baernstein
• Partial Differential Equations of Elliptic Type, eds. A.Alvino et al, Symposia Mathematica, Cambridge Univ.Press, 35:47–91
• 1995

## Baernstein , II . Convolution and rearrangement on the circle

• II Baernstein, B. A. Taylor
• Complex Variables Theory Appl .
• 1989

## Inequalities

• G. H. Hardy, J. E. Littlewood, G. Pólya
• Cambridge Mathematical Library. Cambridge University Press, Cambridge
• 1988
VIEW 2 EXCERPTS

• Mathematics
• 1987
VIEW 1 EXCERPT

VIEW 1 EXCERPT

## II and B

• A. Baernstein
• A. Taylor. Spherical rearrangements, subharmonic functions, and ∗-functions in n-space. Duke Math. J., 43(2):245–268
• 1976
VIEW 1 EXCERPT

• Mathematics
• 1974
VIEW 1 EXCERPT