Functionals for Multilinear Fractional Embedding

被引：29

作者：

Beckner, William ^{[1
]}

机构：

[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2015年 / 31卷 / 01期

关键词：

Fractional embedding; Hardy-Littlewood-Sobolev inequality; diagonal trace restriction; Coulomb interaction; Pitt's inequality; SOBOLEV INEQUALITIES; PITTS INEQUALITY; LAPLACIAN; CONSTANTS;

D O I：

10.1007/s10114-015-4321-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A novel representation is developed as a measure for multilinear fractional embedding. Corresponding extensions are given for the Bourgain-Brezis-Mironescu theorem and Pitt's inequality. New results are obtained for diagonal trace restriction on submanifolds as an application of the Hardy-Littlewood-Sobolev inequality. Smoothing estimates are used to provide new structural understanding for density functional theory, the Coulomb interaction energy and quantum mechanics of phase space. Intriguing connections are drawn that illustrate interplay among classical inequalities in Fourier analysis.

引用

页码：1 / 28

页数：28

共 23 条

[1] Logarithmic Sobolev inequalities and the existence of singular integrals [J].