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Inequalites and properties of some generalized Orlicz classes and spaces. (English) Zbl 1164.26016

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.

MSC:

26D10 Inequalities involving derivatives and differential and integral operators
26D15 Inequalities for sums, series and integrals
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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