ABSTRACT
A proof of Lemma 2 can be found in Rao and Ren ([8], p. 154, p.93). Lemma 3. (Ren [9, Lemma 4.6]) For an N-function , let F be defined
by (4). Suppose that C = lim
exists (C + ). Then = lim
G (u) exists also, where G (u) is as in (5), and
Similarly, if C 0 = lim t
F (t) exists (CO + ), then 0 = lim u 0
G (u) exists and
c0 (9)
For an N-function , the Orliez function space L( ) on = [0, ) or [0, 1] with the usual Lebesgue measure is defined to be the set {x : x is real, Lebesgue measurable on and p ( x) = ( |x(t)\)dt < for some
> 0}. The gauge norm is given by ||x||( ) = inf { c > 0 : p (xc 1}.
