Luca Lorenzi

activity

20132025

collaborators

6 papers

math.AP2025

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

Davide Addona, Vincenzo Leone, Luca Lorenzi +1

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…

math.AP2024

Kernel estimates for parabolic systems of partial differential equations with unbounded coefficients

Davide Addona, Luca Lorenzi, Marianna Porfido

We provide pointwise upper bounds for the transition kernels of semigroups associated with a class of systems of nondegenerate elliptic partial differential equations with unbounde…

math.AP2024

Space Regularity of Evolution Equations Driven by Rough Paths

Davide Addona, Luca Lorenzi, Gianmario Tessitore

In this paper, we consider the linear evolution equation $d y (t) = A y (t) d t + G y (t) d x (t)$ , where $A$ is a closed operator, associated to a semigroup, with good smoothing effects in a Ban…

math.AP2023

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

Davide Addona, Vincenzo Leone, Luca Lorenzi +1

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}…

math.FA2022

Young equations with singularities

D. Addona, L. Lorenzi, G. Tessitore

In this paper we prove existence and uniqueness of a mild solution to the Young equation $d y (t) = A y (t) d t + σ (y (t)) d x (t)$ , $t \in [0, T]$ , $y (0) = ψ$ . Here, $A$ is an unbounded operator whi…

math.AP2013

Kernel estimates for nonautonomous Kolmogorov equations

M. Kunze, L. Lorenzi, A. Rhandi

Using time dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernels of some nonautonomous Kolmogorov operators with possibly unbounded drift and diffusion…

Bounded H∞-calculus for vectorial-valued operators with Gaussian kernel estimates