Related papers: A LYM Inequality For Product Measures

In this paper we shall consider one parametric generalization of some non-symmetric divergence measures. The \textit{non-symmetric divergence measures} are such as: Kullback-Leibler \textit{relative information}, $\chi…

We prove a Fr\"olicher-type inequality for a compact generalized complex manifold $M$, and show that the equality holds if and only if $M$ satisfies the generalized $\partial\bar{\partial}$-Lemma. In particular, this gives a unified proof…

We present a simple proof of Christer Borell's general inequality in the Brunn-Minkowski theory. We then discuss applications of Borell's inequality to the log-Brunn-Minkowski inequality of B\"or\"oczky, Lutwak, Yang and Zhang.

It is well known that jointly measurable observables cannot lead to a violation of any Bell inequality - independent of the state and the measurements chosen at the other site. In this letter we prove the converse: every pair of…

Similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.

In this short note we establish an integral geometric inequality in a smooth metric measure space of the nonnegative Bakry-\'Emery Ricci curvature. This result can be regarded as a mild generalization of the almost Schur theorem due to De…

Let $\pi$ be an irreducible cuspidal automorphic representation of $\text{GL}_n(\mathbb A_\mathbb Q)$ with associated $L$-function $L(s, \pi)$. We study the behaviour of the partial Euler product of $L(s, \pi)$ at the center of the critical…

In this paper, we discuss the Weyl problem in warped product space. We obtain the openness, non rigidity and some applications. These results together with the a priori estimates obtained by Lu imply some existence results. Meanwhile we…

We provide a proof of the sharp log-Sobolev inequality on a compact interval.

We will show certain functional inequalities between some products of $x^p - 1$.

Bell inequalities for number measurements are derived via the observation that the bits of the number indexing a number state are proper qubits. Violations of these inequalities are obtained from the output state of the nondegenerate…

In this paper, we present a general principle for the Lebesgue measure theory of limsup sets defined by rectangles under the hypothesis of ubiquity for rectangles.

In this paper, the concept of the classical $f$-divergence (for a pair of measures) is extended to the mixed $f$-divergence (for multiple pairs of measures). The mixed $f$-divergence provides a way to measure the difference between multiple…

The general versions of the Bohnenblust--Hille inequality for $m$-linear forms are valid for exponents $q_{1},...,q_{m}\in \lbrack 1,2].$ In this show that a slightly different characterization is valid for $q_{1},...,q_{m}\in (0,\infty ).$

The purpose of this short note is to demonstrate uniform logarithmic Sobolev inequalities for the mean field gradient particle systems associated to an energy functional that is convex in the flat sense. A defective log-Sobolev inequality…

Using the log-convexity of the Gamma function and Euler's reflection formula, we give a new proof of a classical weighted sine product inequality. Two different parameter choices yield two competing upper bounds for the same product. We…

In this paper, we obtain inequalities for some integrals involving the modified Lommel function of the first kind $t_{\mu,\nu}(x)$. In most cases, these inequalities are tight in certain limits. We also deduce a tight double inequality,…

\footnotesize B\"{o}r\"{o}czky, Lutwak, Yang and Zhang recently conjectured a certain strengthening of the Brunn-Minkowski inequality for symmetric convex bodies, the so-called log-Brunn-Minkowski inequality. We establish this inequality…

An inequality of Brascamp and Lieb provides a bound on the covariance of two functions with respect to log-concave measures. The bound estimates the covariance by the product of the $L^2$ norms of the gradients of the functions, where the…

The goal of this note is to give, at least for a restricted range of indices, a short proof of homogeneous commutator estimates for fractional derivatives of a product, using classical tools. Both $L^{p}$ and weighted $L^{p}$ estimates can…