A characterization of the inclusion between Lp-spaces is well-known (see for instance [7], [3]). Here we present an analogous characterization for Orlicz Spaces. To this aim we use some definitions of the Orlicz and Luxemburg norms that are a little bit simpler than usual. Also this allows us to extend to Orlicz spaces the well-known property that in a finite measure space the Lp-norm tends to the L1-norm as p → +∞.
Two properties of norms in Orlicz spaces
CARUSO, ANDREA ORAZIO
2003-01-01
Abstract
A characterization of the inclusion between Lp-spaces is well-known (see for instance [7], [3]). Here we present an analogous characterization for Orlicz Spaces. To this aim we use some definitions of the Orlicz and Luxemburg norms that are a little bit simpler than usual. Also this allows us to extend to Orlicz spaces the well-known property that in a finite measure space the Lp-norm tends to the L1-norm as p → +∞.File in questo prodotto:
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