We discuss and complement the knowledge about generalized Orlicz classes <img src="http://www.springerlink.com/content/441p6p4420776gjl/10474_2007_6083_Article_IEq1.gif" /> 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.
NATURVETENSKAP -- Matematik (hsv//swe)
NATURAL SCIENCES -- Mathematics (hsv//eng)
NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)