Functional calculus estimates for Tadmor-Ritt operators

TL;DR

This paper establishes improved $H^{ ext{"}infty}$-functional calculus estimates for Tadmor-Ritt operators, linking these bounds to discrete square function estimates and advancing the understanding of their power-bounds.

Contribution

It provides new, sharper functional calculus estimates for Tadmor-Ritt operators, extending and refining previous results by Vitse.

Findings

Enhanced $H^{ ext{"}infty}$-calculus bounds for Tadmor-Ritt operators

Demonstrated the influence of discrete square function estimates on these bounds

Achieved results aligned with the best known power-bounds

Abstract

We show $H^{\infty}$-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 estimates.