arXiv research

A reverse Riesz estimate and spectral gap imply a Poincaré inequality.

We prove an optimal reverse Poincaré inequality for the heat semigroup generated by the sub-Laplacian on a Carnot group of any step. As an application we give new proofs of the isoperimetric inequality and of the boundedness of the Riesz transform in Carnot groups.

We study the validity of the $L^p$ inequality for the Riesz transform when $p>2$ and of its reverse inequality when $p<2$ on complete Riemannian manifolds under the doubling property and some Poincaré inequalities.

We establish various $L^{p}$ estimates for the Schrödinger operator $-Δ+V$ on Riemannian manifolds satisfying the doubling property and a Poincaré inequality, where $Δ$ is the Laplace-Beltrami operator and $V$ belongs to a reverse Hölder class. At the end of this paper we apply our result on Lie groups with polynomial …

Riesz regression connects to density ratio estimation for causal inference.

Unified framework for debiased machine learning using Riesz representer and Bregman divergence.

Study proves NN matching is equivalent to Riesz regression for debiased machine learning.

Develops a direct debiased machine learning framework using Bregman divergence.

Unified theory for causal inference using various methods.

Gradient boosting estimates Riesz representer for causal inference.

Python package automates causal parameter estimation using Riesz regression.

Two approaches to directly estimating Riesz representer are shown to be numerically equivalent under certain conditions.

Estimates heat kernel gradients on fractal-like cable systems.

Proposes adversarial method to estimate Riesz representer.

In this paper we prove mixed norm estimates for Riesz transforms related to Laplace--Beltrami operators on compact Riemannian symmetric spaces of rank one. These operators are closely related to the Riesz transforms for Jacobi polynomials expansions. The key point is to obtain sharp estimates for the kernel of the Jaco…

The study bounds Riesz transforms on manifolds with controlled curvature.

ScoreMatchingRiesz improves debiased machine learning and policy effects estimation.

Unified framework for estimating density ratios in causal inference.

Let $M$ be a complete non-compact manifold satisfying the volume doubling condition, with doubling index $N$ and reverse doubling index $n$, $n\le N$, both for large balls. Assume a Gaussian upper bound for the heat kernel, and an $L^2$-Poincaré inequality outside a compact set. If $2<n$, then we show that for $p\in (2…

Let $(X,d,μ)$ be a doubling metric measure space endowed with a Dirichlet form $\E$ deriving from a "carré du champ". Assume that $(X,d,μ,\E)$ supports a scale-invariant $L^2$-Poincaré inequality. In this article, we study the following properties of harmonic functions, heat kernels and Riesz transforms for $p\in (2,\i…

Improved AutoDML estimator for causal inference using outcome-adapted shared covariate representation.

Prediction-powered causal inference achieves smaller asymptotic variance than traditional methods.

One considers the class of complete non-compact Riemannian manifolds whose heat kernel satisfies Gaussian estimates from above and below. One shows that the Riesz transform is $L^p$ bounded on such a manifold, for $p$ ranging in an open interval above 2, if and only if the gradient of the heat kernel satisfies a certai…

The paper examines $L^p$ gradient and Riesz transform estimates under Ricci lower bounds.

This is the fourth article of our series. Here, we study weighted norm inequalities for the Riesz transform of the Laplace-Beltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Gaussian upper bounds.

The paper proves boundedness of a Riesz transform on weighted manifolds.

We investigate the boundness of the Riesz transform on $L^p$ for connected sum of manifolds where the Riesz transform is bounded on $L^p$.

The goal of this article is twofold: in a first part, we prove Gaussian estimates for the heat kernel of Schr{ö}dinger operators delta + V whose potential V is "small at infinity" in an integral sense. In a second part, we prove sharp boundedness result for the associated Riesz transform with potential d(delta+V) --1/2…

Using hyperbolic form convolution with doubly isometry-invariant kernels, the explicit expression of the inverse of the de Rham laplacian acting on m-forms in the Poincaré space is found. Also, by means of some estimates for hyperbolic singular integrals, we obtain L^p-estimates for the Riesz transforms passing from th…

Given a sequence of complete Riemannian manifolds $(M_n)$ of the same dimension, we construct a complete Riemannian manifold $M$ such that for all $p \in (1,\infty)$ the $L^p$-norm of the Riesz transform on $M$ dominates the $L^p$-norm of the Riesz transform on $M_n$ for all $n$. Thus we establish the following dichoto…

Let $M$ be a smooth Riemannian manifold which is the union of a compact part and a finite number of Euclidean ends, $\RR^n \setminus B(0,R)$ for some $R > 0$, each of which carries the standard metric. Our main result is that the Riesz transform on $M$ is bounded from $L^p(M) \to L^p(M; T^*M)$ for $1 < p < n$ and unbou…

We show a perturbation result for the boundedness of the Riesz transform : if $M$ and $M_0$ are complete Riemannian manifolds satisfying a Sobolev inequality of dimension $n$, which are isometric outside a compact set, and if the Riesz transform on $M_0$ is bounded on $L^q$, then for all $\frac{n}{n-2}, the Riesz trans…

Paper improves MMD flow efficiency with Riesz kernels for image generation.

We investigate the $L^p$-boundness of the Riesz transform on Riemannian manifolds whose Ricci curvature has quadratic decay. Two criteria for the $L^p$-unboundness of the Riesz transform are given. We recover known results about manifolds that are Euclidean or conical at infinity.

Let $(M^m,g)$ be a m-dimensional complete Riemannian manifold which satisfies the n-Sobolev inequality and on which the volume growth is comparable to the one of $\R^n$ for big balls; if the Hodge Laplacian on 1-forms is strongly positive and the Ricci tensor is in $L^{\frac{n}{2}\pm ε}$ for an $ε>0$, then we prove a G…

Study $L^p$ boundedness of Riesz transform on differential forms for certain manifolds.

Let $M$ be a complete non-compact Riemannian manifold. In this paper, we derive sufficient conditions on metric perturbation for stability of $L^p$-boundedness of the Riesz transform, $p\in (2,\infty)$. We also provide counter-examples regarding in-stability for $L^p$-boundedness of Riesz transform.

Unified framework for causal inference under sample selection.

We show that balls, circles and 2-spheres can be identified by generalized Riesz energy among compact submanifolds of the Euclidean space that are either closed or with codimension 0, where the Riesz energy is defined as the double integral of some power of the distance between pairs of points. As a consequence, we obt…

Estimates for covariant derivatives and Riesz transforms on differential forms.

Graph continuous operators become Riesz continuous after multiplication by unitary operators.

On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that the Atiyah-Singer Dirac operator $\mathrm{D}_{\mathcal B}$ in $\mathrm{L}^{2}$ depends Riesz continuously on $\mathrm{L}^{\infty}$ perturbations of local boundary conditions ${\mathcal B}$. The Lipschitz bound for the map ${…

In this paper we study the Riesz transform on complete and connected Riemannian manifolds $M$ with a certain spectral gap in the $L^2$ spectrum of the Laplacian. We show that on such manifolds the Riesz transform is $L^p$ bounded for all $p \in (1,\infty)$. This generalizes a result by Mandouvalos and Marias and extend…

On an asymptotically conic manifold $(M,g)$, we analyze the asymptotics of the integral kernel of the resolvent $R_q(k):=(Δ_q+k^2)^{-1}$ of the Hodge Laplacian $Δ_q$ on $q$-forms as the spectral parameter $k$ approaches zero, assuming that 0 is not a resonance. The first application we give is an $L^p$ Sobolev estimate…

New method for estimating treatment effects without complex propensity models.

The paper argues for using Neyman orthogonal score for balancing in debiased machine learning.

We construct a large class of Riemannian manifolds of arbitrary dimension with Riesz transform unbounded on $L^p(M)$ for all $p > 2$. This extends recent results for Vicsek manifolds, and in particular shows that fractal structure is not necessary for this property.

Automatic debiasing for causal and policy effects using Neural Nets and Random Forests.