相关论文: Detailed proof of Nazarov's inequality

In this article we prove a multidimensional version of the Nazarov lemma. The proof is based on an appropriate generalisation of the regularised system of intervals introduced by Havin, Nazarov and Mashreghi to several dimensions.

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

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

The main goal of this exposition is to present further analysis of the Kantorovich and Ando operator inequalities. In particular, a new proof of Ando's inequality is given, a new non-trivial refinement of Kantorovich inequality is shown,…

The aim of this paper is to give an overview of some inequalities about $L^p$-norms ($p= 1$ or $p= 2$) of harmonic (periodic) and non-harmonic trigonometric polynomials. Among the material covered, we mention Ingham's Inequality about 2…

We improve constants in the Rademacher-Menchov inequality.

In this paper we present a complete proof of a conjecture due to V. V. Prelov in 2010 about an information inequality for the binary entropy function.

Azuma's inequality is a tool for proving concentration bounds on random variables. The inequality can be thought of as a natural generalization of additive Chernoff bounds. On the other hand, the analogous generalization of multiplicative…

Extending the idea in [Impagliazzo, R., Moore, C. and Russell, A., An entropic proof of Chang's inequality. SIAM Journal on Discrete Mathematics, 28(1), pp.173-176.] we give a short information theoretic proof for Chang's lemma that is…

In this paper we give some sharper refinements and generalizations of inequalities related to Shafer's inequality for the arctangent function, stated in Theorems 1, 2 and 4 in [1], by C. Mortici and H.M. Srivastava.

We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.

Preliminary results from Nathanson [5] are used to prove the Muirhead and Rado inequalities.

We prove some extensions of Andrews inequality.

We give a survey of recent results, due mainly to the authors, concerning Bernstein-Markov type inequalities and connections with potential theory.

Olkin and Shepp (2005, J. Statist. Plann. Inference, vol. 130, pp. 351--358) presented a matrix form of Chernoff's inequality for Normal and Gamma (univariate) distributions. We extend and generalize this result, proving Poincare-type and…

The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].

We provide a new characterization of the logarithmic Sobolev inequality.

The aim of this paper is to provide a self-contained proof of a general case of the coarea inequality, also known as the Eilenberg inequality. The result is known, but we are not aware of any place that a proof would be written with all…

A simple proof of a key inequality required by the paper's analysis is presented. An introductory section discussing the paper's setup may be helpful to some readers. An alternative statistical analysis is suggested.

In this paper we proved a new numerically explicit version of the P\'{o}lya--Vinogradov inequality. Our proof is based on the new ideas of V.A. Bykovskii and improves a recent inequality obtained by C. Pomerance.