A local Landau type inequality for semigroup orbits
Volume 223 / 2014
Studia Mathematica 223 (2014), 19-26
MSC: Primary 47D06; Secondary 26D10.
DOI: 10.4064/sm223-1-2
Abstract
Given a strongly continuous semigroup $(S(t))_{t\ge0}$ on a Banach space $X$ with generator $A$ and an element $f\in D(A^2)$ satisfying $\|S(t)f\|\le e^{-\omega t}\|f\|$ and $\|S(t)A^2f\|$ $\le e^{-\omega t}\|A^2f\|$ for all $t\ge0$ and some $\omega>0$, we derive a Landau type inequality for $\|Af\|$ in terms of $\|f\|$ and $\|A^2f\|$. This inequality improves on the usual Landau inequality that holds in the case $\omega=0$.
