144 Chapter 7

The LP Spaces: Completeness and Approximation

14. Show that if f (x ) = In( 1/x) for x e (0, 1], then f belongs to LP(0, 1] for all 1 lt; p lt; oo but

does not belong to Lo ( 0, 1].

15. Formulate and prove an extension of Holder’s Inequality for the product of three functions

16. Suppose that ( f. I is bounded in /

110 11 Is If

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