Related papers: A sharp commutator estimate for all Riesz modulate…
Let $R_j$ denote the $j^{\text{th}}$ Riesz transform on $\mathbb{R}^n$. We prove that there exists an absolute constant $C>0$ such that \begin{align*} |\{|R_jf|>\lambda\}|\leq C\left(\frac{1}{\lambda}\|f\|_{L^1(\mathbb{R}^n)}+\sup_{\nu}…
We consider a generalization of the Riesz operator in $R^d$ and obtain estimates for its norm and for related capacities via the modified Wolff potential. These estimates are based on the certain version of $T1$ theorem for…
In the present paper, the Complex Ginzburg-Landau-Schr\"odinger (CGLS) equation with the Riesz fractional derivative has been treated by a reliable implicit finite difference method (IFDM) of second order and furthermore for the purpose of…
For general dimension $d$ we prove the equidistribution of energy at the micro-scale in $\mathbb R^d$, for the optimal point configurations appearing in Coulomb gases at zero temperature. At the microscopic scale, i.e. after blow-up at the…
We obtain strong consistency and asymptotic normality of a least squares estimator of the drift coefficient for complex-valued Ornstein-Uhlenbeck processes disturbed by fractional noise, extending the result of Y. Hu and D. Nualart,…
This article deals with Coulomb gases at an intermediate temperature regime, in which no structure is observed at the microscopic level, but the mass in confined to a compact set. Our main result is a concentration inequality around the…
This paper presents the nonlinear potential theory for mixed local and nonlocal $p$-Laplace type equations with coefficients and measure data, involving both superquadratic and subquadratic cases. We prove a class of universal pointwise…
In this paper, we propose a new framework named Communication Optimal Transport (CommOT) for computing the rate distortion (RD) function. This work is motivated by observing the fact that the transition law and the relative entropy in…
For a general Calderon-Zygmund operator $T$ on $R^N$, it is shown that $\|Tf\|_{L^2(w)}\leq C(T)\|w\|_{A_2}\|f\|_{L^2(w)}$ for all Muckenhoupt weights $w\in A_2$. This optimal estimate was known as the $A_2$ conjecture. A recent result of…
In this paper, we derive a strong convergence rate of spatial finite difference approximations for both focusing and defocusing stochastic cubic Schr\"odinger equations driven by a multiplicative $Q$-Wiener process. Beyond the uniform…
In this work we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the…
This paper presents a unified approach to the modeling and computation of the Kubo conductivity of incommensurate bilayer heterostructures at finite temperature. Firstly, we derive an expression for the large-body limit of Kubo-Greenwood…
In this note we prove a sharp reverse weak estimate for Riesz potentials $$\|I_{s}(f)\|_{L^{\frac{n}{n-s},\infty}}\geq \gamma_sv_{n}^{\frac{n-s}{n}}\|f\|_{L^1}~~\text{for}~~0<f\in {L^1(\mathbb{R}^n)},$$ where…
We investigate the relationship between the covariant and the three-dimensional (equal-time) formulations of quantum kinetic theory. We show that the three-dimensional approach can be obtained as the energy average of the covariant…
In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of R^n. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams' results to…
We dominate non-integral singular operators by adapted sparse operators and derive optimal norm estimates in weighted spaces. Our assumptions on the operators are minimal and our result applies to an array of situations, whose prototype are…
The main purpose of this paper is to establish weighted estimates for singular integrals associated with Zygmund dilations via a discrete Littlewood--Paley theory, and then apply it to obtain the upper bound of the norm of commutators of…
The Gromov-Wasserstein (GW) variant of optimal transport, designed to compare probability densities defined over distinct metric spaces, has emerged as an important tool for the analysis of data with complex structure, such as ensembles of…
Given a closed submanifold, or a compact regular domain, in euclidean space, we consider the Riesz energy defined as the double integral of some power of the distance between pairs of points. When this integral diverges, we compare two…
We study asymptotic shape optimization for Riesz means of Robin Laplacian eigenvalues among cuboids of fixed measure. Our focus is the regime where the Robin parameter is proportional to the square root of the spectral parameter defining…