Some properties of functions in Orlicz space

For functions in Orlicz space L _M ^* , we study the behavior of (t)dt, where x^* (t) is non-increasing and equimeasurable with ¦ x(t) ¦. We establish the existence of unbounded functions in L _M ^* that are not limits of bounded functions and for which . Moreover, we establish a new criterion for an N-function to belong to the class ₂ and a sufficiency test for a function to belong to Orlicz space.Translated from Matematicheskie Zametki, Vol. 3, No. 2, pp. 145–156, February, 1968.