Publication at Faculty of Mathematics and Physics |
2017
Abstract
We study the necessity of bump conditions for the boundedness of the Hardy-Littlewood maximal operator between weighted L-p spaces with different weights. The conditions in question are obtained by replacing the L-p' average of sigma(1/p)' in the Muckenhoupt A(p)-condition by an average with respect to a stronger Banach function norm, and are known to be sufficient for the two-weighted maximal inequality.
We show that these conditions are in general not necessary for such an inequality to be true.