Journal of Inequalities and Applications
Volume 5 (2000), Issue 4, Pages 309-320
A general rearrangement inequality à la Hardy–Littlewood
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 smooth on with for . Furthermore, let nonnegative and bounded functions on with compact support. We prove the inequality , where denotes symmetric decreasing rearrangement.