Kallman–Rota inequality

In mathematics, the Kallman–Rota inequality, introduced by (Kallman Rota), is a generalization of the Landau–Kolmogorov inequality to Banach spaces. It states that if A is the infinitesimal generator of a one-parameter contraction semigroup then

[math]\displaystyle{ \|Af\|^2 \le 4\|f\|\|A^2f\|. }[/math]

References

• Kallman, Robert R. (1970), "On the inequality [math]\displaystyle{ \Vert f^{\prime} \Vert^{2}\leqq4\Vert f\Vert\cdot\Vert f''\Vert }[/math]", Inequalities, II (Proc. Second Sympos., U.S. Air Force Acad., Colo., 1967), New York: Academic Press, pp. 187–192 .