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/