Some properties of functions in Orlicz space |
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Authors: | D. V. Salekhov |
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Affiliation: | (1) Voronezh Engineering-Construction Institute, USSR |
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Abstract: | For functions in Orlicz space LM*, 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 LM* 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. |
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