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Suppose $1, then show $L^{p_1}[a,b] \supset L^{p_2}[a,b]$.

I was able to show $\|f\|_{p_1} \le \|f\|_{p_2} (b-a)^{1/p_1 - 1/p_2}$ but I'm not sure how to proceed from here.

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    Hint: Jensen's inequality.2011-02-11
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    Well, your inequality shows that if $\|f\|_2$ is finite, then so is $\|f\|_1$, what else do you want?2011-02-11
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    Sorry, you must have already used something like Jensen's inequality to get what you have so far. But aren't you almost there? If you have an inequality then that helps you compare when the norms are finite.2011-02-11
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    oh haha sorry that was silly of me.2011-02-11

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