It is shown that if T is a sublinear translation invariant operator of restricted weak type (1,1) acting on L¹(𝕋), then T maps simple functions in L log L(𝕋) boundedly into L¹(𝕋).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-2-4, author = {Paul Alton Hagelstein}, title = {Orlicz bounds for operators of restricted weak type}, journal = {Colloquium Mathematicae}, volume = {103}, year = {2005}, pages = {193-197}, zbl = {1086.42009}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-2-4} }
Paul Alton Hagelstein. Orlicz bounds for operators of restricted weak type. Colloquium Mathematicae, Tome 103 (2005) pp. 193-197. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-2-4/