Kallman–Rota inequality

In mathematics, the Kallman–Rota inequality, introduced by Kallman & Rota (1970), 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

‖ A f ‖ 2 ≤ 4 ‖ f ‖ ‖ A 2 f ‖ . {\displaystyle \|Af\|^{2}\leq 4\|f\|\|A^{2}f\|.}

References

  • Kallman, Robert R.; Rota, Gian-Carlo (1970), "On the inequality ‖ f ′ ‖ 2 ≦ 4 ‖ f ‖ ⋅ ‖ f ″ ‖ {\displaystyle \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, MR 0278059.