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.
@article{10_4064_sm165_3_6,
author = {Jiecheng Chen and Xiangrong Zhu},
title = {A note on the strong maximal operator on ${\Bbb R}^n$},
journal = {Studia Mathematica},
pages = {291--294},
year = {2004},
volume = {165},
number = {3},
doi = {10.4064/sm165-3-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm165-3-6/}
}
TY - JOUR
AU - Jiecheng Chen
AU - Xiangrong Zhu
TI - A note on the strong maximal operator on ${\Bbb R}^n$
JO - Studia Mathematica
PY - 2004
SP - 291
EP - 294
VL - 165
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4064/sm165-3-6/
DO - 10.4064/sm165-3-6
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%A Xiangrong Zhu
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%J Studia Mathematica
%D 2004
%P 291-294
%V 165
%N 3
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Jiecheng Chen; Xiangrong Zhu. A note on the strong maximal operator on ${\Bbb R}^n$. Studia Mathematica, Tome 165 (2004) no. 3, pp. 291-294. doi: 10.4064/sm165-3-6
