Orlicz Uzayının Tanımı Üzerine Bir Not

Abstract

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 �ݔ ௣ � 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.