Inequalites and properties of some generalized Orlicz classes and spaces (Q955177)

The generalized Orlicz classes \(\widetilde{X}_{\Phi}\) and generalized Orlicz spaces \(X_{\Phi}\) are defined by replacing the space \(L^{1}\) in the classical construction of Orlicz classes \(\widetilde{L}_{\Phi }\) and Orlicz spaces \(L_{\Phi }\) by an arbitrary Banach function space \(X.\) The authors prove some results which are important for the study of inequalities in these spaces. In particular, they prove some natural generalizations of the classical Minkowski's inequality, Hölder's inequality and Young's inequality.