Journal of Inequalities and Applications
Volume 5 (2000), Issue 4, Pages 309-320

A general rearrangement inequality à la Hardy–Littlewood

Friedemann Brock

Universität Leipzig, Fakultät für Mathematik und Informatik,, Augustusplatz 10, Leipzig D-04109, Germany

Received 5 May 1999; Revised 12 July 1999

Copyright © 2000 Friedemann Brock. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let F=F(v1,,vm) smooth on (R0+)m with Fvivj0 for ij. Furthermore, let u1,,um nonnegative and bounded functions on Rn with compact support. We prove the inequality RnF(u1,,um)dxRnF(u1,,um)dx, where denotes symmetric decreasing rearrangement.