An exact expression for the down norm is given in terms of the level function on all rearrangement invariant spaces and a useful approximate expression is given for the down norm on all rearrangement invariant spaces whose upper Boyd index is not one.
@article{urn:eudml:doc:41424, title = {The level function in rearrangement invariant spaces.}, journal = {Publicacions Matem\`atiques}, volume = {45}, year = {2001}, pages = {175-198}, mrnumber = {MR1829583}, zbl = {0987.46033}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41424} }
Sinnamon, Gord. The level function in rearrangement invariant spaces.. Publicacions Matemàtiques, Tome 45 (2001) pp. 175-198. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41424/