## Illinois Journal of Mathematics

### 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.

#### Article information

Source
Illinois J. Math., Volume 56, Number 3 (2012), 759-793.

Dates
First available in Project Euclid: 31 January 2014

https://projecteuclid.org/euclid.ijm/1391178547

Digital Object Identifier
doi:10.1215/ijm/1391178547

Mathematical Reviews number (MathSciNet)
MR3161350

Zentralblatt MATH identifier
1309.42025

Subjects
Primary: 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 28D05: Measure-preserving transformations

#### Citation

Moonens, Laurent; Rosenblatt, Joseph M. Moving averages in the plane. Illinois J. Math. 56 (2012), no. 3, 759--793. doi:10.1215/ijm/1391178547. https://projecteuclid.org/euclid.ijm/1391178547

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