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# Computations for Nonsquare Constants of Orlicz spaces

DOI link for Computations for Nonsquare Constants of Orlicz spaces

Computations for Nonsquare Constants of Orlicz spaces book

# Computations for Nonsquare Constants of Orlicz spaces

DOI link for Computations for Nonsquare Constants of Orlicz spaces

Computations for Nonsquare Constants of Orlicz spaces book

## 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}.