Functionals for Multilinear Fractional Embedding

TL;DR

This paper introduces a new measure for multilinear fractional embedding, extending classical inequalities and applying them to quantum mechanics and density functional theory, revealing deep connections in Fourier analysis.

Contribution

It develops a novel measure for multilinear fractional embedding and extends key inequalities, offering new insights into quantum mechanics and Fourier analysis.

Findings

Extended Bourgain-Brezis-Mironescu theorem

New results on diagonal trace restriction

Enhanced understanding of Coulomb energy and phase space

Abstract

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.