## The properties of functions from $W_{2}^{1}$ [closed]

Is it true that the product of the two functions from $W_{2}^{1}(0,1)$ belongs to $W_{2}^{1}(0,1)$?

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yes, because they are in $L^\infty$ with derivative in $L^2$, and $(uv)'=uv'+u'v$. – Pietro Majer Jun 14 at 10:45