Maximal regularity under quadratic estimates

TL;DR

This paper explores a harmonic analysis approach to maximal regularity in evolution equations, emphasizing invariance properties and quadratic estimates to unify forward and backward maximal regularity operators.

Contribution

It introduces invariance properties of maximal regularity operators within a harmonic analysis framework, extending the understanding of their behavior under quadratic estimates.

Findings

Establishes invariance properties of maximal regularity operators

Provides a unified approach to forward and backward maximal regularity

Highlights the role of quadratic estimates and functional calculi

Abstract

In this Short Note we complement the intriguing harmonic analytic perspective due to P. Auscher and A. Axelsson for the abstract evolution equations. This concerns a unified approach to temporally weighted estimates for the forward and backward maximal regularity operators in presence of quadratic estimates and functional calculi. In particular we provide several invariance properties for the maximal regularity operators either in evolution form or in balayage form.