We prove Kato inequalities involving Dirac operators, suggesting newfound applications across various contexts.
We prove, for a class of first order differential operators containing generalized gradients, the Dirac and Penrose twistor operators, a family of Kato inequalities that interpolates between the classical and the refined Kato inequalities. For the Hodge-de-Rham operator we get a more detailed result. As applications, we obtain various Kato inequalities from the literature.
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Cibotaru et al. (2025) studied this question.
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