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/