A note on the strong maximal operator on ${\Bbb R}^n$
Volume 165 / 2004
Studia Mathematica 165 (2004), 291-294
MSC: Primary 42B25; Secondary 42B35.
DOI: 10.4064/sm165-3-6
Abstract
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 $E$ of finite measure.
