Related papers: An operator-coefficients free Poincar\'e inequalit…

Let $\mathscr{R}$ be a collection of disjoint dyadic rectangles $R$ with sides parallel to the axes, let $\pi_R$ denote the non-smooth bilinear projection onto $R$ \[ \pi_R (f,g)(x):=\iint \mathbf{1}_{R}(\xi,\eta) \widehat{f}(\xi)…

With direct and simple proofs, we establish Poincar\'{e} type inequalities (including Poincar\'{e} inequalities, weak Poincar\'{e} inequalities and super Poincar\'{e} inequalities), entropy inequalities and Beckner-type inequalities for…

This paper provides a discrete Poincar\'e inequality in $n$ space dimensions on a simplex $K$ with explicit constants. This inequality bounds the norm of the piecewise derivative of functions with integral mean zero on $K$ and all integrals…

In this note we prove a Wiener criterion of regularity of boundary points for the Dirichlet problem related to $X$-elliptic operators in divergence form enjoying the doubling condition and the Poincar\'e inequality. As a step towards this…

For a polynomial $P$ mapping the integers into the integers, define an averaging operator $A_{N} f(x):=\frac{1}{N}\sum_{k=1}^N f(x+P(k))$ acting on functions on the integers. We prove sufficient conditions for the $\ell^{p}$-improving…

In this paper we establish a Hermite- Hadamard type inequality for operator preinvex functions and an estimate of the right hand side of a Hermite- Hadamard type inequality in which some operator preinvex functions of selfadjoint operators…

Let $\Phi$ be a unital positive linear map and let $A$ be a positive invertible operator. We prove that there exist partial isometries $U$ and $V$ such that \[ |\Phi(f(A))\Phi(A)\Phi(g(A))|\leq U^*\Phi(f(A)Ag(A))U \] and…

We study hypoelliptic operators with polynomially bounded coefficients that are of the form K = sum_{i=1}^m X_i^T X_i + X_0 + f, where the X_j denote first order differential operators, f is a function with at most polynomial growth, and…

By a result of Lundquist-Barrett, it follows that the rank of a positive semi-definite matrix is less than or equal to the sum of the ranks of its principal diagonal submatrices when written in block form. In this article, we take a general…

In this short note, we provide a quantitative global Poincar\'e inequality for one forms on a closed Riemannian four manifold, in terms of an upper bound on the diameter, a positive lower bound on the volume, and a two-sided bound on Ricci…

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…

In this paper, we prove that, in dimension one, the Poincar\'e inequality is equivalent to a new transport-chi-square inequality linking the square of the quadratic Wasserstein distance with the chi-square pseudo-distance. We also check…

On a prequantizable K\"ahler manifold $(M, \omega, L)$, Chan-Leung-Li constructed a genuine (non-asymptotic) action of a subalgebra of the Berezin-Toeplitz star product on $H^0(M, L^{\otimes k})$ for each level $k$ [14]. We extend their…

Let $\M$ be a smooth connected manifold endowed with a smooth measure $\mu$ and a smooth locally subelliptic diffusion operator $L$ which is symmetric with respect to $\mu$. We assume that $L$ satisfies a generalized curvature dimension…

Let $f:M \to \mathbb{R}$ be a Morse-Bott function on a compact smooth finite dimensional manifold $M$. The polynomial Morse inequalities and an explicit perturbation of $f$ defined using Morse functions $f_j$ on the critical submanifolds…

Operator-valued multivariable Bohr type inequalities are obtained for: a class of noncommutative holomorphic functions, generalizing the analytic functions on the open unit disc; the noncommutative disc algebra and the noncommutative…

The aim of this paper is to establish various functional inequalities for the convolution of a compactly supported measure and a standard Gaussian distribution on Rd. We especially focus on getting good dependence of the constants on the…

We first define the trace on a domain $\Omega$ which is definable in an o-minimal structure. We then show that every function $u\in W^{1,p}(\Omega)$ vanishing on the boundary in the trace sense satisfies Poincar\'e inequality. We finally…

Via a random construction we establish necessary conditions for $L^p(\ell^q)$ inequalities for certain families of operators arising in harmonic analysis. In particular we consider dilates of a convolution kernel with compactly supported…

In this paper, we present some operator and eigenvalue inequalities involving operator monotone, doubly concave and doubly convex functions. These inequalities provide some variants of operator Acz\'{e}l inequality and its reverse via…