Tommaso Bruno

activity

20162026

most citedSchrödinger operators on Lie groups with purely discrete spectrum

4 citations · 8 across the 13 of their papers we have counts for

collaborators

20 papers

math.FA2026

Function spaces for weighted subcoercive operators

Tommaso Bruno, Mattia Calzi, Marco M. Peloso

We develop a theory of Sobolev, Besov and Triebel--Lizorkin spaces associated with weighted subcoercive operators on any real connected Lie group.

math.AP2023

Pointwise convergence to initial data for some evolution equations on symmetric spaces

Tommaso Bruno, Effie Papageorgiou

Let $L$ be either the Laplace--Beltrami operator, its shift without spectral gap, or the distinguished Laplacian on a symmetric space of noncompact type $X$ of a…

math.CA2023

Hardy spaces and dilations on homogeneous groups

Tommaso Bruno, Jordy Timo van Velthoven

On a homogeneous group, we characterize the one-parameter groups of dilations whose associated Hardy spaces in the sense of Folland and Stein are the same.

math.FA2023

Pointwise multipliers for Triebel--Lizorkin and Besov spaces on Lie groups

Tommaso Bruno, Marco M. Peloso, Maria Vallarino

On a general Lie group $G$ endowed with a sub-Riemannian structure and of local dimension $d$ , we characterize the pointwise multipliers of Triebel--Lizorkin spaces $F_{α}^{p, q}$ for…

math.FA2022

Optimal heat kernel bounds and asymptotics on Damek--Ricci spaces

Tommaso Bruno, Federico Santagati

We give optimal bounds for the radial, space and time derivatives of arbitrary order of the heat kernel of the Laplace--Beltrami operator on Damek--Ricci spaces. In the case of sym…

math.FA2021★ 4 cited

Schrödinger operators on Lie groups with purely discrete spectrum

Tommaso Bruno, Mattia Calzi

On a Lie group $G$ , we investigate the discreteness of the spectrum of Schrödinger operators of the form $L + V$ , where $L$ is a subelliptic sub-Laplacian on $G$ …

math.FA2021★ 1 cited

Local and nonlocal Poincaré inequalities on Lie groups

Tommaso Bruno, Marco M. Peloso, Maria Vallarino

We prove a local $L^{p}$ -Poincaré inequality, $1 \leq p < \infty$ , on noncompact Lie groups endowed with a sub-Riemannian structure. We show that the constant involved grows at most e…

math.FA2021

Homogeneous algebras via heat kernel estimates

Tommaso Bruno

We study homogeneous Besov and Triebel--Lizorkin spaces defined on doubling metric measure spaces in terms of a self-adjoint operator whose heat kernel satisfies Gaussian estimates…

math.FA2020

The Sobolev embedding constant on Lie groups

Tommaso Bruno, Marco M. Peloso, Maria Vallarino

In this paper we estimate the Sobolev embedding constant on general noncompact Lie groups, for sub-Riemannian inhomogeneous Sobolev spaces endowed with a left invariant measure. Th…

math.FA2019

Estimates for matrix coefficients of representations

Tommaso Bruno, Michael G. Cowling, Fabio Nicola +1

Estimates for matrix coefficients of unitary representations of semisimple Lie groups have been studied for a long time, starting with the seminal work by Bargmann, by Ehrenpreis a…

math.FA2019

On the Riesz Transforms for the inverse Gauss measure

Tommaso Bruno, Peter Sjögren

Let $γ_{- 1}$ be the absolutely continuous measure on $R^{n}$ whose density is the reciprocal of a Gaussian function. Let further $A$ be the natural self-adjoint La…

math.FA2019

Potential spaces on Lie groups

Tommaso Bruno, Marco M. Peloso, Maria Vallarino

In this paper we discuss function spaces on a general noncompact Lie group, namely the scales of Triebel--Lizorkin and Besov spaces, defined in terms of a sub-Laplacian with drift.…

math.FA2019

Besov and Triebel--Lizorkin spaces on Lie groups

Tommaso Bruno, Marco M. Peloso, Maria Vallarino

In this paper we develop a theory of Besov and Triebel--Lizorkin spaces on general noncompact Lie groups endowed with a sub-Riemannian structure. Such spaces are defined by means o…

math.FA2018★ 2 cited

Maximal Hypoellipticity for Left-Invariant Differential Operators on Lie Groups

Tommaso Bruno

Given a differential operator defined in terms of left-invariant vector fields on a Lie group, we prove that the local condition defining maximal hypoellipticity is equivalent to a…

math.FA2018

Sobolev spaces on Lie groups: embedding theorems and algebra properties

Tommaso Bruno, Marco M. Peloso, Anita Tabacco +1

Let $G$ be a noncompact connected Lie group, denote with $ρ$ a right Haar measure and choose a family of linearly independent left-invariant vector fields $X$ on $G$ satis…

math.FA2018

Singular integrals and Hardy type spaces for the inverse Gauss measure

Tommaso Bruno

Let $γ_{- 1}$ be the absolutely continuous measure on $R^{n}$ whose density is the reciprocal of a Gaussian and consider the natural weighted Laplacian $A$ on $L^2(…

math.FA2018

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

Tommaso Bruno

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 Orns…

math.CA2017

Asymptotics for the Heat Kernel on H-Type Groups

Tommaso Bruno, Mattia Calzi

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…

math.FA2016★ 1 cited

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

Tommaso Bruno, Mattia Calzi

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}…

math.FA2016

Endpoint results for Fourier integral operators on noncompact symmetric spaces

Tommaso Bruno, Anita Tabacco, Maria Vallarino

Let X be a noncompact symmetric space of rank one and let h^1(X) be a local atomic Hardy space. We prove the boundedness from h^1(X) to L^1(X) and on h^1(X) of some classes of Four…