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

$\Vert Af{\Vert }^2\le 4\Vert f\Vert \Vert A^{2}f\Vert .$

References

• Kallman, Robert R. (1970), "On the inequality $\Vert f^{\prime }{\Vert }^2\leqq 4\Vert f\Vert \cdot \Vert f^{″}\Vert$", Inequalities, II (Proc. Second Sympos., U.S. Air Force Acad., Colo., 1967), New York: Academic Press, pp. 187–192 .