Maximal inequalities and Riesz transforms for vector-valued magnetic Schrödinger operators

We consider vector-valued magnetic Schrödinger operators $-{\mathbf{\Delta }}_{\mathit{a}}+V$ with magnetic potential $\mathit{a}\in L_{\mathrm{l}\mathrm{o}\mathrm{c}}^2({\mathbb{R}}^d;{\mathbb{R}}^d)$ and electric potential $V$ given by a matrix-valued function whose entries belong to $L_{\mathrm{l}\mathrm{o}\mathrm{c}}^1({\mathbb{R}}^d)$. We prove maximal inequalities in $L^p({\mathbb{R}}^d;{\mathbb{C}}^m)$, $p\in [1,\mathrm{\infty })$ and the boundedness of the Riesz transforms $(\mathrm{\nabla }-i\mathit{a})(-{\mathbf{\Delta }}_{\mathit{a}}+V{)}^{-\frac{1}{2}}$ and $V^{\alpha }(-{\mathbf{\Delta }}_{\mathit{a}}+V{)}^{-\alpha }$ on $L^p({\mathbb{R}}^d;{\mathbb{C}}^m)$ for every $p\in (1,2]$ and every $\alpha \in [0,1\mathrm{/}p]$.