Extended Kato inequalities for conformal operators

TL;DR

This paper develops a family of Kato inequalities for conformal operators, including Dirac and Penrose twistor operators, providing a unified framework that encompasses classical and refined inequalities, with detailed results for the Hodge-de-Rham operator.

Contribution

It introduces a new family of Kato inequalities for a broad class of first order differential operators, unifying and extending previous results.

Findings

Derived a family of Kato inequalities for conformal operators

Unified classical and refined Kato inequalities within a single framework

Obtained detailed inequalities for the Hodge-de-Rham operator

Abstract

We prove, for a class of first order differential operators containing the generalized gradients, Dirac and Penrose twistor operators, a family of Kato inequalities that interpolates between the classical and the refined Kato. For the Hodge-de-Rham operator we get a more detailed result. As a corollary, we get various Kato inequalities from the literature.