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A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.

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If a function is in a Sobolev space, what can we say about its square?

If I have a function $f \in H^s(\mathbb R^n)$, what can I say about $f^2$? In particular, I'm interested in the case when $s < 0$ and would like to conclude that, for example, $f \in H^{2s}(\mathbb R^ …
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