Averaging on $n$-dimensional rectangles

Abstract

In this work we investigate families of translation invariant differentiation bases $B$ of rectangles in $R^n$, for which $L{\log }^{n-1}L(R^n)$ is the largest Orlicz space that $B$ differentiates. In particular, we improve on techniques developed by A.~Stokolos 1988 and 2008.

17 pages, 2 figures