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Hello,

If a function, say u, is smooth and L^2 on R^n. Will it be bounded??

In the case of n=1 I would say that it obviously is so. Because if it were unbounded then it wouldn't be L^2.

But in the case of n=2 (or higher). I can imagine a function with a kind of ridge that gets thinner and thinner but higher and higher, the further away from the origin we get. So that it would be unbounded but still L^2.

I guess I was just wondering if this line of thinking is correct? Thankful for any feedback.

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# Smooth and L^2 on R^n. Will it be bounded?

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