G. Dall’Ara

activity

20132026

most citedAn optimal multiplier theorem for Grushin operators in the plane, I

6 citations · 29 across the 23 of their papers we have counts for

collaborators

25 papers

math.AP2026

Obstructions to exact regularity of sublaplacians

Gian Maria Dall'Ara

Let $M$ be a closed manifold equipped with a collection of smooth real vector fields $X_{1}, \dots, X_{k}$ and a smooth measure $μ$ . Let $P := \sum_{j} X_{j}^{†} X_{j}$ be the associated…

math.MG2026

Exponential improvements in Rado's covering problem

Gian Maria Dall'Ara, Adrian Dumitrescu

Let $B^{d}$ denote the $d$ -dimensional Euclidean ball of unit radius. What is the largest constant $f (B^{d}) \in [0, 1]$ with the property that every finite collection $C$ of…

math.MG2026

Rado's covering problem for cubes and balls: a semi-survey

Gian Maria Dall'Ara, Adrian Dumitrescu

What is the largest constant $c \in [0, 1]$ with the property that every finite collection $C$ of axis-parallel squares in the plane admits a disjoint sub-collection $\math…

math.GT2026

Bounded cohomology classes from differential forms

Gian Maria Dall'Ara, Roberto Frigerio, Ervin Hadziosmanovic

Let $M$ be a complete hyperbolic $n$ -manifold, $n \geq 2$ . Via integration over geodesic simplices, any closed bounded differential 2-form on $M$ defines a bounded cohomology class…

math.CA2025

On the best constant in the finitary Vitali covering lemma for high dimensional cubes

Gian Maria Dall'Ara

Let $Γ_{d}$ be the largest constant such that every finite collection of cubes in $R^{d}$ whose sides are parallel to the coordinate axes admits a disjoint sub-collection occu…

math.CV2025

The Levi $q$ -core and Property ( $P_{q}$ )

Gian Maria Dall'Ara, Samuele Mongodi, John N. Treuer

We introduce the Grassmannian $q$ -core of a distribution of subspaces of the tangent bundle of a smooth manifold. This is a generalization of the concept of the core previously int…

math.AP2024

On generalized Dirichlet integrals in the smooth and in the o-minimal setting

Gian Maria Dall'Ara

Given a compact manifold $M$ equipped with smooth vector fields $X_{1}, \dots, X_{r}$ , we consider the generalized Dirichlet energy \[\mathbf{E}(f)= \sum_{j=1}^r\int_M |X_jf|^2\, dm,\]…

math.CV2024

Higher dimensional worm domains

Simone Calamai, Gian Maria Dall'Ara

We show how to construct a class of smooth bounded pseudoconvex domains whose boundary contains a given Stein manifold with strongly pseudoconvex boundary, having a prescribed codi…

math.CV2023

Sharp subelliptic estimates in the $\partial ˉ$ -Neumann problem via an uncertainty principle

Gian Maria Dall'Ara, Samuele Mongodi

The problem of giving a (CR-)geometric description of the best possible order of a subelliptic estimate at a boundary point in the $\partial ˉ$ -Neumann problem is largely open. I…

math.CV2023

Remarks on the Levi core

Gian Maria Dall'Ara, Samuele Mongodi

We investigate a few aspects of the notion of Levi core, introduced by the authors in a previous work: a basic finiteness question, the connections with Kohn's algorithm and with C…

math.CV2022

An extremality property of Szegő projections on Heisenberg groups

Gian Maria Dall'Ara, Bernhard Lamel

We prove that Heisenberg groups, a.k.a. the boundaries of Siegel domains, minimize the $L^{p}$ operator norm of the Szegő projection in a large class of weighted CR manifolds of hype…

math.CV2022★ 4 cited

Worm domains are not Gromov hyperbolic

Leandro Arosio, Gian Maria Dall'Ara, Matteo Fiacchi

We show that Worm domains are not Gromov hyperbolic with respect to the Kobayashi distance.

math.CV2022★ 3 cited

Nonabelian ramified coverings and $L^{p}$ -boundedness of Bergman projections in $C^{2}$

Gian Maria Dall'Ara, Alessandro Monguzzi

In this work we explore the theme of $L^{p}$ -boundedness of Bergman projections of domains that can be covered, in the sense of ramified coverings, by "nice" domains (e.g. strictly p…

math.CV2021★ 2 cited

An upper bound for the first positive eigenvalue of the Kohn Laplacian on Reinhardt real hypersurfaces

Gian Maria Dall'Ara, Duong Ngoc Son

A real hypersurface in $C^{2}$ is said to be Reinhardt if it is invariant under the standard $T^{2}$ -action on $C^{2}$ . Its CR geometry can be described in ter…

math.CA2021★ 5 cited

An optimal multiplier theorem for Grushin operators in the plane, II

Gian Maria Dall'Ara, Alessio Martini

In a previous work we proved a spectral multiplier theorem of Mihlin--Hörmander type for two-dimensional Grushin operators $- \partial_{x}^{2} - V (x) \partial_{y}^{2}$ , where $V$ is a doubl…

math.CV2021

The core of the Levi distribution

Gian Maria Dall'Ara, Samuele Mongodi

We introduce a new geometrical invariant of CR manifolds of hypersurface type, which we dub the "Levi core" of the manifold. When the manifold is the boundary of a smooth bounded p…

math.AP2021★ 6 cited

An optimal multiplier theorem for Grushin operators in the plane, I

Gian Maria Dall'Ara, Alessio Martini

Let $L = - \partial_{x}^{2} - V (x) \partial_{y}^{2}$ be the Grushin operator on $R^{2}$ with coefficient $V : R \to [0, \infty)$ . Under the sole assumptions that $V…

math.CV2021

Around $L^{1}$ (un)boundedness of Bergman and Szegö projections

Gian Maria Dall'Ara

We consider the problem of $L^{1}$ (un)boundedness for a wide class of orthogonal projections, including Bergman projections on domains in complex manifolds and Szegö projections on…

math.AP2017★ 5 cited

A robust approach to sharp multiplier theorems for Grushin operators

Gian Maria Dall'Ara, Alessio Martini

We prove a multiplier theorem of Mihlin-Hörmander type for operators of the form $- Δ_{x} - V (x) Δ_{y}$ on $R_{x}^{d_{1}} \times R_{y}^{d_{2}}$ , where $V(x) = \sum_{j=1}^{d_1}…

math.CV2017★ 2 cited

On noncompactness of the $\partial$ -Neumann problem on pseudoconvex domains in $C^{3}$

Gian Maria Dall'Ara

In this paper we deal with the following question: is it true that any bounded smooth pseudoconvex domain in $C^{n}$ whose boundary contains a $q$ -dimensional complex manifo…

math.CV2015★ 1 cited

Coercivity of weighted Kohn Laplacians: the case of model monomial weights in $C^{2}$

Gian Maria Dall'Ara

The weighted Kohn Laplacian $□_{φ}$ is a natural second order elliptic operator associated to a weight $φ : C^{n} \to R$ and acting on $(0, 1)$ -forms, which pla…

math.CV2015

Pointwise estimates of weighted Bergman kernels in several complex variables

Gian Maria Dall'Ara

We prove new pointwise bounds for weighted Bergman kernels in $C^{n}$ , whenever a coercivity condition is satisfied by the associated weighted Kohn Laplacian on $(0, 1)$ -form…

math.CV2015★ 1 cited

Matrix Schrödinger Operators and Weighted Bergman Kernels

Gian Maria Dall'Ara

The aim of the present thesis is twofold: to study the problem of discreteness of the spectrum of Schrödinger operators with matrix-valued potentials in $R^{d}$ (Chapter 1)…

math.SP2014

Discreteness of the spectrum of Schrödinger operators with non-negative matrix-valued potentials

Gian Maria Dall'Ara

We prove three results giving sufficient and/or necessary conditions for discreteness of the spectrum of Schrödinger operators with non-negative matrix-valued potentials, i.e., ope…

Obstructions to exact regularity of sublaplacians

Exponential improvements in Rado's covering problem

Rado's covering problem for cubes and balls: a semi-survey

Bounded cohomology classes from differential forms

On the best constant in the finitary Vitali covering lemma for high dimensional cubes

The Levi q-core and Property (Pq​)

On generalized Dirichlet integrals in the smooth and in the o-minimal setting

Higher dimensional worm domains

Sharp subelliptic estimates in the ∂ˉ-Neumann problem via an uncertainty principle

Remarks on the Levi core

An extremality property of Szegő projections on Heisenberg groups

Worm domains are not Gromov hyperbolic

Nonabelian ramified coverings and Lp-boundedness of Bergman projections in C2

An upper bound for the first positive eigenvalue of the Kohn Laplacian on Reinhardt real hypersurfaces

An optimal multiplier theorem for Grushin operators in the plane, II

The core of the Levi distribution

An optimal multiplier theorem for Grushin operators in the plane, I

Around L1 (un)boundedness of Bergman and Szegö projections

A robust approach to sharp multiplier theorems for Grushin operators

On noncompactness of the ∂-Neumann problem on pseudoconvex domains in C3

Coercivity of weighted Kohn Laplacians: the case of model monomial weights in C2

Pointwise estimates of weighted Bergman kernels in several complex variables

Matrix Schrödinger Operators and Weighted Bergman Kernels

Discreteness of the spectrum of Schrödinger operators with non-negative matrix-valued potentials

The Levi $q$ -core and Property ( $P_{q}$ )

Sharp subelliptic estimates in the $\partial ˉ$ -Neumann problem via an uncertainty principle

Nonabelian ramified coverings and $L^{p}$ -boundedness of Bergman projections in $C^{2}$

Around $L^{1}$ (un)boundedness of Bergman and Szegö projections

On noncompactness of the $\partial$ -Neumann problem on pseudoconvex domains in $C^{3}$

Coercivity of weighted Kohn Laplacians: the case of model monomial weights in $C^{2}$