2017/06/08 by Michael Christ, Christ, Michael
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1706.02778
openalex publication_date 2017/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An inequality of Brascamp-Lieb-Luttinger generalizes the Riesz-Sobolev inequality, stating that certain multilinear functionals, acting on nonnegative functions of one real variable with prescribed distribution functions, are maximized when these functions are symmetrized. It is shown that under certain hypotheses, when the functions are indicator functions of sets of prescribed measures, then up to the natural translation symmetries of the inequality, the maximum is attained only by intervals centered at the origin. Moreover, a quantitative form of this uniqueness is established, sharpening the inequality. The hypotheses include an auxiliary genericity assumption which may not be necessary.