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Open Access Open Badges Research Article

A general rearrangement inequality à la Hardy–Littlewood

Friedemann Brock

Author Affiliations

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

Journal of Inequalities and Applications 2000, 2000:805282  doi:10.1155/S1025583400000151

The electronic version of this article is the complete one and can be found online at: http://www.journalofinequalitiesandapplications.com/content/2000/4/805282


Received:5 May 1999
Revisions received:12 July 1999

© 2000 Brock

Let smooth on with for . Furthermore, let nonnegative and bounded functions on with compact support. We prove the inequality , where denotes symmetric decreasing rearrangement.

Keywords:
Symmetrization; Rearrangement; Integral inequality