Can anyone give me examples of functions in one space but not another?(adsbygoogle = window.adsbygoogle || []).push({});

For instance, some f(x) with f(x) in L2 but not in L1?

The best I can come up with so far is:

f(x) = 1/sqrt(x). Thus is unbounded at 0, but would be in L1 since its integral on 0 to 1 is bounded.

But I can't seem to come up with any examples of a function that would be in L2 but not L1. I've tried polynomial, trig, and some complex functions.

Also, it appears that Ln for some finite n is "larger" than Linfinity. This seems to follow from my above example, since that f(x) wouldn't be in Linfinity but would be in L1, right?

But if Linfinity is the limit of Ln as n goes to infinity, then there must be some inflection point where some Lm is "smaller" than the Ln for m > n.

Is this accurate?

Or is it that L1 is "larger" than L2? This makes more sense, for 1/sqrt(x) is in L1. But (1/sqrt(x))^2 = 1/x is not in L2. So f(x) is not in L2.

thanks

brian

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# Lp space examples

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