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I’m trying to prove that there is a constant $ \space C>0 \space$ such that for any function $ \space u \in C^{\infty}_{0} \left ( \mathbb{R} \right ) \space$ following inequality holds: $ {\left \| u \right \|}_{L^2 \left ( \mathbb{R} \right )} \leq C {\left \| u’ \right \|}^{1/2}_{L^1 \left ( \mathbb{R} \right )}Read more