Growth rate of eventually positive Kreiss bounded $$C_0$$-semigroups on $$L^p$$ and $$\mathcal {C}(K)$$

Abstract

Let T be a strongly Kreiss bounded linear operator on L p . We obtain a somewhat optimal control on the rate of growth of the norms ofthe powers. The proof makes use of Fourier multipliers, in particular of Littlewwod-Paley inequalities on arbitrary intervals as initiated by Rubio de Francia and developped by Kislyakov and Parilov.