Inequalities that sharpen the triangle inequality for sums of $N$ functions in $L^p$

Rupert L. Frank (Mathematisches Institut, Ludwig-Maximilans Universität München, Germany; and California Institute of Technology (Caltech), Pasadena, Calif., U.S.A.)

Elliott H. Lieb (Departments of Mathematics and Physics, Princeton University, Princeton, New Jersey, U.S.A.)

Abstract

We study $L^p$ inequalities that sharpen the triangle inequality for sums of $N$ functions in $L^p$.

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Work partially supported by NSF grants DMS-1501007 (E.A.C.) and DMS-1363432 (R.L.F.).

Received 26 March 2019

Received revised 14 July 2019

Accepted 25 November 2019

Published 21 July 2022