English

A note on a theorem of M. Christ

Analysis of PDEs 2019-09-11 v1 Classical Analysis and ODEs Functional Analysis

Abstract

This note is a supplement to our paper `Proof of spherical flocking based on quantitative rearrangement inequalities'. Recently, M. Christ has derived a deep result concerning stability of the Riesz rearrangement inequality. We are interested in the special case of this inequality where two of the sets are equal and the third set is a fixed ball. We show that in this special case, Christ's proof extends with only minor changes to the case where characteristic functions are replaced by functions taking values between zero and one.

Keywords

Cite

@article{arxiv.1909.04598,
  title  = {A note on a theorem of M. Christ},
  author = {Rupert L. Frank and Elliott H. Lieb},
  journal= {arXiv preprint arXiv:1909.04598},
  year   = {2019}
}

Comments

18 pages, supplement to our paper `Proof of spherical flocking based on quantitative rearrangement inequalities'

R2 v1 2026-06-23T11:11:24.878Z