# On the growth rate of powers of a strongly Kreiss bounded operator on $L^p$-spaces

## TL;DR

This paper establishes an optimal polynomial bound on the growth rate of powers of strongly Kreiss bounded operators on $L^p$-spaces, utilizing Fourier multipliers and Littlewood-Paley inequalities.

## Contribution

It provides the first optimal polynomial growth bound for powers of strongly Kreiss bounded operators on $L^p$-spaces, employing advanced harmonic analysis techniques.

## Key findings

- Optimal polynomial growth bound established
- Utilizes Fourier multipliers and Littlewood-Paley inequalities
- Advances understanding of operator power behavior on $L^p$-spaces

## Abstract

Let $T$ be a strongly Kreiss bounded linear operator on $L^p$. We obtain a bound on the rate of growth of the norms of the powers of $T$. The bound is optimal with respect to the polynomial scale. The proof makes use of Fourier multipliers, in particular of the Littlewood-Paley inequalities on arbitrary intervals as initiated by Rubio de Francia and developed by Kislyakov and Parilov.