# Limiting absorption principle and Strichartz estimates for Dirac operators in two and higher dimensions

## TL;DR

This paper establishes a limiting absorption principle and derives Strichartz estimates for Dirac operators in multiple dimensions with potentials, under certain spectral and decay conditions, advancing understanding of their spectral and dispersive properties.

## Contribution

It proves a limiting absorption principle for Dirac operators with potentials in higher dimensions, leading to new dispersive estimates for the associated linear equations.

## Key findings

- Proved a limiting absorption principle for Dirac operators with potentials.
- Derived Strichartz estimates for the Dirac equation in multiple dimensions.
- Addressed challenges with large potentials where free resolvent decay is insufficient.

## Abstract

In this paper we consider Dirac operators in $\mathbb R^n$, $n\geq2$, with a potential $V$. Under mild decay and continuity assumptions on $V$ and some spectral assumptions on the operator, we prove a limiting absorption principle for the resolvent, which implies a family of Strichartz estimates for the linear Dirac equation. For large potentials the dynamical estimates are not an immediate corollary of the free case since the resolvent of the free Dirac operator does not decay in operator norm on weighted $L^2$ spaces as the frequency goes to infinity.