A Note On The Defininiton of An Orlicz Space

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The Orlicz spaces were introduced by Z.W. Birnbaum and W. Orlicz in 1931 as a natural generalization of the classical Lebesgue spaces. For this generalization the function x^p entering in the definition of Lebesgue s space is replaced by a more general convex function Ф. Until today, Orlicz spaces have been studied by many authors from a different aspects. But, most of these studies used different definitions for the convex function Ф to define the Orlicz spaces. In this paper we will investigate the exact relationships between these different definitions of convex functions Ф and obtain the differences between the corresponding Orlicz spaces.

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Orlicz space , N , Function , Young function , Orlicz function , Lebesgue space

Afyon Kocatepe University Journal Of Science an‎d Engineering

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Afyon Kocatepe University Journal Of Science an‎d Engineering