Related papers: Widom factors for generalized Jacobi measures

We give weighted norm inequalities for the maximal fractional operator $ \mathcal M_{q,\beta}$ of Hardy-Littlewood and the fractional integral $I_{\gamma}$. These inequalities are established between $(L^{q},L^{p}) ^{\alpha}(X,d,\mu)$…

We use cosmological constraints from current data sets and a figure of merit (FoM) approach to probe any deviations from general relativity (GR) at cosmological scales. The FoM approach is used to study the constraining power of various…

We deal with the boundedness properties of higher order commutators related to some generalizations of the multilinear fractional integral operator of order $m$, $I_\alpha ^m$, from a product of weighted Lebesgue spaces into adequate…

We determine which sets saturate the Szeg}o and Schiefermayr lower bounds on the norms of Chebyshev Polynomials. We also discuss sets that saturate the Totik--Widom upper bound.

We give the first positive formulas for the weights of every simple highest weight module $L(\lambda)$ over an arbitrary Kac-Moody algebra. Under a mild condition on the highest weight, we also express the weights of $L(\lambda)$ as an…

The purpose of this article is to give a Chlodowsky type generalization of Szasz operators defined by means of the Sheffer type polynomials. We obtain convergence properties of our operators with the help of Korovkin's theorem and the order…

Let $H\subset \R^{d+1}$ be a compact, convex, analytic hypersurface of finite type with a smooth measure $\sigma $ on $H$. Let $\kappa$ denote the Gaussian curvature on $H$. We consider the oscillatory integral $(\kappa^{1/2}…

Given two n-dimensional measures $\mu$ and $\nu$ on Polish spaces, we propose an optimal transportation's formulation, inspired by classical Kan-torovitch's formulation in the scalar case. In particular, we established a strong duality…

Let $G$ denotes a finite abelian group of order $n$ and Davenport constant $D$, and put $m= n+D-1$. Let $x=(x_1, ..., x_m)\in G^m$ be a sequence with a maximal repetition $\ell$ attained by $x_m$ and put $r=\min(D,\ell)$. Let $w=(w_1, ...,…

We aim at studying the asymptotic properties of typical positive braids, respectively positive dual braids. Denoting by $\mu_k$ the uniform distribution on positive (dual) braids of length $k$, we prove that the sequence $(\mu_k)_k$…

We consider the case of hyperbolic basic sets $\Lambda$ of saddle type for holomorphic maps $f: \mathbb P^2\mathbb C \to \mathbb P^2\mathbb C$. We study equilibrium measures $\mu_\phi$ associated to a class of H\"older potentials $\phi$ on…

We prove matching direct and inverse theorems for (algebraic) polynomial approximation with doubling weights $w$ having finitely many zeros and singularities (i.e., points where $w$ becomes infinite) on an interval and not too ``rapidly…

In this note we show that in metric measure spaces satisfying the reduced curvature-dimension condition CD*(K,N) we always have geodesics in the Wasserstein space of probability measures that satisfy the critical convexity inequality of…

We show that skew-orthogonal functions, defined with respect to Jacobi weight $w_{a,b}(x)={(1-x)}^a{(1+x)}^b$, $a$, $b>-1$, including the limiting cases of Laguerre ($w_{a}(x)=x^{a}e^{-x}$, $a > -1$) and Gaussian weight ($w(x)=e^{-x^2}$),…

Exact upper and lower bounds on the ratio $\mathsf{E}w(\mathbf{X}-\mathbf{v})/\mathsf{E}w(\mathbf{X})$ for a centered Gaussian random vector $\mathbf{X}$ in $\mathbb{R}^n$, as well as bounds on the rate of change of…

For "Riesz-like" kernels $K(x,y)=f(|x-y|)$ on $A\times A$, where $A$ is a compact $d$-regular set $A\subset \mathbb{R}^p$, we prove a minimum principle for potentials $U_K^\mu=\int K(x,y)d\mu(x)$, where $\mu$ is a Borel measure supported on…

Let $T_1$, $T_2$ be two Calder\'on-Zygmund operators and $T_{1,\,b}$ be the commutator of $T_1$ with symbol $b\in {\rm BMO}(\mathbb{R}^n)$. In this paper, the author prove that, the composite operator $T_1T_2$ satisfies the following…

Let (M,g) a compact Riemannian $n$-dimensional manifold with umbilic boundary. It is well know that, under certain hypothesis, in the conformal class of g there are scalar-flat metrics that have the boundary of M as a constant mean…

Let $G$ be a connected compact group equipped with the normalised Haar measure $\mu$. Our first result shows that given $\alpha, \beta>0$, there is a constant $c = c(\alpha,\beta)>0$ such that for any compact sets $A,B\subseteq G$ with $…

A set-system $S\subseteq \{0,1\}^n$ is cube-ideal if its convex hull can be described by capacity and generalized set covering inequalities. In this paper, we use combinatorics, convex geometry, and polyhedral theory to give exponential…