5
$\begingroup$

Landau inequality is about the bounds of derivatives of a real(complex)-valued function defined on some interval of the real line (I heard this from a lecture). I learned the simplest case is: $$ \| f' \|_{L^\infty (-\infty,+\infty)}^2 \leq 4 \|f\| \cdot \|f''\| ,$$ the later norms are the same as the first one. I tried several functions $f$, and they are indeed the case, yet I don't have any idea how to get the general result (or the proof).

Can someone be kind enough to give me some hints on this? Besides, does this inequality have similar results on finite intervals? Can someone give me some references on this? Thank you very much!

2 Answers 2