Monday, July 24, 2023 — 3:00 pm — aula M1.6, edificio Matematica
Maximal $L^p$ inequalities for vector-valued Schrödinger operators
Abstract: In this talk we prove various $L^p$-estimates for vector-valued Schrödinger operators of the form $\mathcal L \mathbf{u} := −\Delta \mathbf{u} + V\mathbf{u}$, where $V: \: \mathbb R^d \to \mathcal S(m)$ and $\mathcal S(m)$ is the set of all $m \times m$ symmetric matrices. We assume reverse Hölder estimates on the minimal eigenvalue $\lambda_V(\cdot)$ of $V$ and show some results of Auscher-Ben Ali in the vector-valued case.
The main tools are improved vector-valued Fefferman-Phong inequalities and $L^1$-estimates for weak solutions of $\mathcal L$ and their gradients.
The talk is based on a joint work with D. Addona, V. Leone and L. Lorenzi.