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

Loris Arnold; Christophe Cuny

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arXiv · 2302.14135

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

Loris Arnold·Christophe Cuny

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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.

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Loris Arnold, Christophe Cuny. 2023-02-27. On the growth rate of powers of a strongly Kreiss bounded operator on $L^p$-spaces. https://arxiv.org/abs/2302.14135

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