arXiv subjects

Vincenzo Leone

Publications and source records attributed to Vincenzo Leone.

3 recordsLinked to original sources

arXiv2026

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

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

math.AP↗

arXiv2025

Bounded $H^\infty$-calculus for vectorial-valued operators with Gaussian kernel estimates

We prove that the vector-valued generator of a bounded holomorphic semigroup represented by a kernel satisfying Gaussian estimates with bounded $H^\infty$-calculus in $L^2(\mathbb R^d;\mathbb C^m)$ admits bounded $H^\infty$-calculus for every $p\in (1,\infty)$. We apply this result to the elliptic operator $-{\rm div}(Q\nabla)+V$, where the potential term V is a matrix-valued function whose entries belong to $L^1_{\rm loc}(\mathbb R^d)$ and, for almost every $x\in \mathbb R^d$, $V(x)$ is a symmetric and nonnegative definite matrix.

math.AP↗

arXiv2023

$L^p$ Maximal regularity for vector-valued Schrödinger operators

In this paper we consider the vector-valued Schrödinger operator $-Δ+ V$, where the potential term $V$ is a matrix-valued function whose entries belong to $L^1_{\rm loc}(\mathbb{R}^d)$ and, for every $x\in\mathbb{R}^d$, $V(x)$ is a symmetric and nonnegative definite matrix, with non positive off-diagonal terms and with eigenvalues comparable each other. For this class of potential terms we obtain maximal inequality in $L^1(\mathbb{R}^d,\mathbb{R}^m).$ Assuming further that the minimal eigenvalue of $V$ belongs to some reverse Hölder class of order $q\in(1,\infty)\cup\{\infty\}$, we obtain maximal inequality in $L^p(\mathbb{R}^d,\mathbb{R}^m)$, for $p$ in between $1$ and some $q$.

math.AP↗