DIFFERENtIAl & DIFFERENCE EqUAtIONS ANd APPlICAtIONS

REARRANGEMENT ON THE UNIT BALL FOR FUNCTIONS
WITH MEAN VALUE ZERO WITH APPLICATIONS
TO SOBOLEV AND MOSER INEQUALITIES
MARK LECKBAND
A rearrangement and properties are discussed, as well as the application to the proof of
the corresponding Sobolev and Moser inequalities.
Copyright © 2006 Mark Leckband. 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.
1. Introduction
Rearranging a function to a more simpler form is a standard tool of analysis. The rearranged
function is normally equimeasurable to the original function, hence the L p norms
for 1 ≤ p