Moving averages in the plane

Abstract

We study the almost everywhere behavior of the maximal operator associated to moving averages in the plane, both for Lebesgue derivatives and ergodic averages. We show that the almost everywhere behavior of the maximal operator associated to a sequence of moving rectangles $v_{i}+Q_{i}$, with $(0,0)\in Q_{i}$, depends both on the way the rectangles are moved by $v_{i}$ and the structure of the rectangles ($Q_{i}$) as a partially ordered set.