Related papers: Khinchin-type inequalities via Hadamard's factoris…
In this paper, we establish some Harnack type inequalities satisfied by positive solutions of nonlocal inhomogeneous equations arising in the description of various phenomena ranging from population dynamics to micro-magnetism. For regular…
We establish a Schur--Horn type inequality for symmetric hyperbolic polynomials. As an immediate consequence, we resolve a conjecture of Nam Q. Le on Hadamard-type inequalities for hyperbolic polynomials. Our argument is based on the…
We prove disjointification inequalities due to Johnson and Schechtman for noncommutative random variables independent in the sense of Junge and Xu. In the same setting, we also prove noncommutative Khinchine inequalities. These inequalities…
We define enumerative invariants associated to a hybrid Gauged Linear Sigma Model. We prove that in the relevant special cases, these invariants recover both the Gromov-Witten type invariants defined by Chang-Li and Fan-Jarvis-Ruan using…
In the present paper, we establish some new fractional integral inequalities similar to P$\acute{o}$lya-Szeg$\ddot{o}$ integral inequality and fractional inequality related to Minkowsky inequality by using the Hadamard fractional integral…
We survey some of the mechanisms used to prove that naturally defined sequences in combinatorics are log-concave. Among these mechanisms are Alexandrov's inequality for mixed discriminants, the Alexandrov Fenchel inequality for mixed…
A generalization of classical determinant inequalities like Hadamard's inequality and Fischer's inequality is studied. For a version of the inequalities originally proved by Arveson for positive operators in von Neumann algebras with a…
Majorization inequalities for symmetric polynomials have interested mathematicians for centuries, from the AM-GM inequality for two variables going back at least to Euclid, through classical results of Newton, Muirhead and Gantmacher, to…
We consider convex solutions of nonlinear elliptic equations which satisfy the structure condition of Bian-Guan. We prove a weak Harnack inequality for the eigenvalues of the Hessian of these solutions. This can be viewed as a quantitative…
We sharpen the moment comparison inequalities with sharp constants for sums of random vectors uniform on Euclidean spheres, providing a deficit term (optimal in high dimensions).
The Duffin--Schaeffer Conjecture answers a question on how well one can approximate irrationals by rational numbers in reduced form (an imposed condition) where the accuracy of the approximation depends on the rational number. It can be…
We derive the sharp constants for the inequalities on the Heisenberg group H^n whose analogues on Euclidean space R^n are the well known Hardy-Littlewood-Sobolev inequalities. Only one special case had been known previously, due to…
We consider Khintchine type inequalities on the $p$-th moments of vectors of $N$ $k$-wise independent Rademacher random variables. We show that an analogue of Khintchine's inequality holds, with a constant $N^{1/2-k/2p}$, when $k$ is even.…
Eigenvalues inequalities involving (log) convex/concav functions and Hermitian matrices, positive unital maps are considered. Simple proofs of Bhatia-Kittaneh inequality and Naimark dilation theorem are given.
In this paper, we established some new Hadamard-type integral inequalities for functions whose derivatives of absolute values are m-convex and ({\alpha},m)-convex functions via Riemann-Liouville fractional integrals.
An analogue of the convergence part of the Khintchine-Groshev theorem, as well as its multiplicative version, is proved for nondegenerate smooth submanifolds in $\mathbb{R}^n$. The proof combines methods from metric number theory with a new…
We provide several results on the diophantine properties of continued fractions on the Heisenberg group, many of which are analogous to classical results for real continued fractions. In particular, we show an analog of Khinchin's theorem…
We explore and generalize a Cauchy-Schwarz-type inequality originally proved in [Electronic Journal of Linear Algebra 35, 156-180 (2019)]: $\|\mathbf{v}^2\|\|\mathbf{w}^2\| - \langle\mathbf{v}^2,\mathbf{w}^2\rangle \leq…
We obtain new proofs with improved constants of the Khintchine-type inequality with matrix coefficients in two cases. The first case is the Pisier and Lust-Piquard noncommutative Khintchine inequality for $p=1$, where we obtain the sharp…
Let $d,k$ be natural numbers and let $\mathcal{L}_1, \dots, \mathcal{L}_k \in \mathrm{GL}_d(\mathbb{Q})$ be linear transformations such that there are no non-trivial subspaces $U, V \subseteq \mathbb{Q}^d$ of the same dimension satisfying…