arXiv subjects

Tommaso Bruno

Publications and source records attributed to Tommaso Bruno.

22 records · Page 2Linked to original sources

arXiv2018

Singular integrals and Hardy type spaces for the inverse Gauss measure

Let $γ_{-1}$ be the absolutely continuous measure on $\mathbb{R}^n$ whose density is the reciprocal of a Gaussian and consider the natural weighted Laplacian $\mathcal{A}$ on $L^2(γ_{-1})$. In this paper, we prove boundedness and unboundedness results for the purely imaginary powers and the first order Riesz transforms associated with the translated operators $\mathcal{A}+λI$, $λ\geq0$, from certain new Hardy-type spaces adapted to $γ_{-1}$ to $L^1(γ_{-1})$. We also investigate the weak type $(1,1)$ of these operators.

math.FA↗

arXiv2018

Endpoint results for the Riesz transform of the Ornstein-Uhlenbeck operator

In this paper we introduce a new atomic Hardy space $X^1(γ)$ adapted to the Gauss measure $γ$, and prove the boundedness of the first order Riesz transform associated with the Ornstein-Uhlenbeck operator from $X^1(γ)$ to $L^1(γ)$. We also provide a new, short and almost self-contained proof of its weak-type $(1,1)$.

math.FA↗

arXiv2017

Asymptotics for the Heat Kernel on H-Type Groups

We give sharp asymptotic estimates at infinity of all radial partial derivatives of the heat kernel on H-type groups. As an application, we give a new proof of the discreteness of the spectrum of some natural sub-Riemannian Ornstein-Uhlenbeck operators on these groups.

math.CA↗

arXiv2016

Weighted sub-Laplacians on Métivier Groups: Essential Self-Adjointness and Spectrum

Let $G$ be a Métivier group and let $N$ be any homogeneous norm on $G$. For $α>0$ denote by $w_α$ the function $e^{-N^α}$ and consider the weighted sub-Laplacian $\mathcal{L}^{w_α}$ associated with the Dirichlet form $ϕ\mapsto \int_{G} |\nabla_\mathcal{H}ϕ(y)|^2 w_α(y)\, dy$, where $\nabla_\mathcal{H}$ is the horizontal gradient on $G$. Consider $\mathcal{L}^{w_α}$ with domain $C_c^\infty$. We prove that $\mathcal{L}^{w_α}$ is essentially self-adjoint when $α\geq 1$. For a particular $N$, which is the norm appearing in $\mathcal{L}$'s fundamental solution when $G$ is an H-type group, we prove that $\mathcal{L}^{w_α}$ has purely discrete spectrum if and only if $α>2$, thus proving a conjecture of J. Inglis.

math.FA↗