A note on the strong maximal operator on R<sup>n</sup>
A note on the strong maximal operator on R<sup>n</sup>
We prove that for $f\in L\mathop {\rm ln}\nolimits ^{+}L({\mathbb R}^n)$ with compact support, there is a $g\in L\mathop {\rm ln}\nolimits ^{+}L({\mathbb R}^n)$ such that (a) $g$ and $f$ are equidistributed, (b) $M_S(g)\in L^1(E)$ for any measurable set $