Abstract
We discuss and complement the knowledge about generalized Orlicz classes \( \tilde X_\Phi \) and Orlicz spaces X Φ obtained by replacing the space L 1 in the classical construction by an arbitrary Banach function space X. Our main aim is to focus on the task to study inequalities in such spaces. We prove a number of new inequalities and also natural generalizations of some classical ones (e.g., Minkowski’s, Hölder’s and Young’s inequalities). Moreover, a number of other basic facts for further study of inequalities and function spaces are included.
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Jain, P., Persson, L.E. & Upreti, P. Inequalities and properties of some generalized Orlicz classes and spaces. Acta Math Hung 117, 161–174 (2007). https://doi.org/10.1007/s10474-007-6083-9
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DOI: https://doi.org/10.1007/s10474-007-6083-9
Key words and phrases
- inequalities
- function spaces
- Orlicz class
- Orlicz space
- Luxemburg norm
- Banach function space
- Young function
- Young’s inequality
- Minkowski’s inequality
- Hölder’s inequality