MOVING AVERAGES IN THE PLANE

摘要

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) ∈ 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.