turkmath.org

Let $ G $ be a locally compact group with left Haar measure $ \mu $ and $ \Phi $ be a Young function. We will consider the Orlicz space $ L^\Phi(G) $ as an$ L^1(G) $- module. If we take $ \Phi(x)=\frac{x^p}{p} $ ,$ 1 \leq p < \infty $, $ L^\Phi(G) $ becomes the classical Lebesgue space $ L^p(G) $. \\In this talk we study the closed convex left invariant subsets of $ L^\Phi(G) $ and characterize affine mappings for Orlicz space. Finally we apply the results to the study of multipliers of $ L^\Phi(G) $. These results generalize classical results on $ L^p $ spaces. This is a joint work with Serap Oztop.