Functional calculus estimates for Tadmor–Ritt operators

We show H∞H∞-functional calculus estimates for Tadmor–Ritt operators (also known as Ritt operators), which generalize and improve results by Vitse. These estimates are in conformity with the best known power-bounds for Tadmor–Ritt operators in terms of the constant dependence. Furthermore, it is shown how discrete square function estimates influence the functional calculus estimates.