A necessary and sufficient condition is given on the basis of a rare maximal function such that implies f ∈ L log L([0,1]).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-1-4,
author = {Paul Alton Hagelstein},
title = {A note on rare maximal functions},
journal = {Colloquium Mathematicae},
volume = {96},
year = {2003},
pages = {49-51},
zbl = {1047.42014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-1-4}
}
Paul Alton Hagelstein. A note on rare maximal functions. Colloquium Mathematicae, Tome 96 (2003) pp. 49-51. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm95-1-4/