Related papers: A note on the Menchov-Rademacher Inequality

In this article, we study the further refinements and reverses of the Young and Heinz inequalities with the Kantorovich constant. These modified inequalities are used to establish corresponding operator inequalities on Hilbert space and…

We obtain some new inequalities of Chebyshev Type.

Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases, we show that we obtain the best possible constant or that our bounds are tight in certain limits. We…

In what follows we improve an inequality related to matrix theory. T. Laffey proved (2013) a weaker form of this inequality [2].

We revisit and slightly modify the proof of the Gaussian Hanson-Wright inequality where we keep track of the absolute constant in its formulation.

To estimate the optimal constant in Hardy-type inequalities, some variational formulas and approximating procedures are introduced. The known basic estimates are improved considerably. The results are illustrated by typical examples. It is…

We address the optimal constants in the strong and the weak Stechkin inequalities, both in their discrete and continuous variants. These inequalities appear in the characterization of approximation spaces which arise from sparse…

In this work we provide the best constants of the multiple Khintchine inequality. This allows us, among other results, to obtain the best constants of the mixed $\left( \ell_{\frac{p}{p-1}},\ell_{2}\right) $-Littlewood inequality, thus…

Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.

We make explicit a theorem of Fromm and Goldmakher [arXiv:1706.03002], which states that one can improve Burgess' bound for short character sums simply by improving the leading constant in the P\'{o}lya-Vinogradov inequality. Towards…

For discrete martingale-difference sequences $d=\{d_1,\ldots,d_n\}$ we consider Khintchine type inequalities, involving certain square function $\mathfrak S (d)$ considered by Chang-Wilson-Wolff in 1982. In particular, we prove…

We prove a stability version of the Pr\'ekopa-Leindler inequality.

We provide new estimates on the best constant of the Lieb-Thirring inequality for the sum of the negative eigenvalues of Schr\"odinger operators, which significantly improve the so far existing bounds.

We give lower bounds on the case of worst inhomogeneous approximation.

This note has a twofold purpose. To improve the best known lower estimates of the Hardy-Littlewood inequality for $m$-linear forms in $\ell_{p}$ spaces and to provide a closed formula encompassing the cases $p>2m$ and $% p=2m.$ Our approach…

The aim of this note is twofold. Firstly, we prove an abstract version of the Calder\'on transference principle for inequalities of admissible type in the general commutative multilinear and multiparameter setting. Such an operation does…

In this article, we establish an improvement of the Cauchy-Schwarz inequality. Let $x, y \in \mathcal{H},$ and let $f: (0,1) \rightarrow \mathbb{R}^+$ be a well-defined function, where $\mathbb{R}^+$ denote the set of all positive real…

We compute the optimal constant for a generalized Hardy-Sobolev inequality, and using the product of two symmetrizations we present an elementary proof of the symmetries of some optimal functions. This inequality was motivated by a…

In this article, we obtain two interesting general inequalities concerning Riemman sums of convex functions, which in particular, sharpen Alzer's inequality and give a suitable converse for it.

The main purpose of this short note, on the one hand, to is rigorize some part of the proof of Theorem 1.3 in [11] in a simple way, and on the other hand, to give an alternative argument from local inequalities to global ones.