Related papers: Testing conditions for multilinear Radon-Brascamp-…

We prove a range of $L^p$ bounds for singular Brascamp-Lieb forms with cubical structure. We pass through sparse and local bounds, the latter proved by an iteration of Fourier expansion, telescoping, and the Cauchy-Schwarz inequality. We…

The Borell-Brascamp-Lieb inequality is a classical extension of the Pr\'ekopa-Leindler inequality, which in turn is a functional counterpart of the Brunn-Minkowski inequality. The stability of these inequalities has received significant…

We give sharp conditions for the limiting Korn-Maxwell-Sobolev inequalities \begin{align*} \lVert P\rVert_{{\dot{W}}{^{k-1,\frac{n}{n-1}}}(\mathbb{R}^n)}\le…

We prove intertwining relations by twisted gradients for Markov semi-groups. These relations are applied to Brascamp-Lieb type inequalities and spectral gap results. It generalizes the results of [1] from the Euclidean space to Riemannian…

H\"older-Brascamp-Lieb inequalities provide upper bounds for a class of multilinear expressions, in terms of $L^p$ norms of the functions involved. They have been extensively studied for functions defined on Euclidean spaces.…

The purpose of this paper is to prove the L^p boundedness of singular Radon transforms and their maximal analogues. These operators differ from the traditional singular integrals and maximal functions in that their definition at any point x…

This paper considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by $p$, is possibly much larger than the sample size $n$. There is a variety of economic applications where solving this…

We consider probability measures on the real line or unit circle with Jacobi or Verblunsky coefficients satisfying an $\ell^p$ condition and a generalized bounded variation condition. This latter condition requires that a sequence can be…

Let $U$ be a bounded domain in $\mathbb C^d$ and let $L^p_a(U)$, $1 \leq p < \infty$, denote the space of functions that are analytic on $\overline{U}$ and bounded in the $L^p$ norm on $U$. A point $x \in \overline{U}$ is said to be a…

In this paper we study some properties of the torsion function with Robin boundary conditions. Here we write the shape derivative of the $L^{\infty}$ and $L^p$ norms, for $p\ge 1$, of the torsion function, seen as a functional on a bounded…

We present a novel analysis of a Radon transform, $R$, which maps an $L^2$ function of compact support to its integrals over smooth surfaces of revolution with centers on an embedded hypersurface in $\mathbb{R}^n$. Using microlocal…

In this paper we are proving the existence of a nontrivial solution of the ${p}(x)$- Laplacian equation with Dirichlet boundary condition. We will use the variational method and concentration compactness principle involving positive radon…

We study Nevai's condition from the theory of orthogonal polynomials on the real line. We prove that a large class of measures with unbounded Jacobi parameters satisfies Nevai's condition locally uniformly on the support of the measure away…

In the paper [G1] the author proved $L^p$ Sobolev regularity results for averaging operators over hypersurfaces and connected them to associated Newton polyhedra. In this paper, we use rather different resolution of singularities techniques…

Given observations from a positive random variable contaminated by multiplicative measurement error, we consider a nonparametric goodness-of-fit testing task for its unknown density in a non-asymptotic framework. We propose a testing…

Bernstein inequalities and inverse theorems are a recent development in the theory of radial basis function(RBF) approximation. The purpose of this paper is to extend what is known by deriving $L^p$ Bernstein inequalities for RBF networks…

We establish a structure theorem for the Brascamp--Lieb constant formulated in the general setting of locally compact abelian groups. This extends and unifies the finiteness characterisations previously known for euclidean spaces and for…

In this paper, we derive sharp nonlinear dimension-free Brascamp--Lieb inequalities (including hypercontractivity inequalities) for distributions on Polish spaces, which strengthen the classic Brascamp--Lieb inequalities. Applications…

Modern applications require a robust and theoretically solid tool for the realistic modeling of electronic states in low dimensional nanostructures. The $k \cdot p$ theory has fruitfully served this role for the long time since its…

We analyze some properties of the measures in the dual of the space $BV$, by considering (signed) Radon measures satisfying a perimeter bound condition, which means that the absolute value of the measure of a set is controlled by the…