Related papers: A note on the Menchov-Rademacher Inequality

In this short note, we improve the famous Reid Inequality related to linear operators.

We prove some extensions of Andrews inequality.

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

We obtain a series improvement to higher-order $L^p$-Rellich inequalities on a Riemannian manifold $M$. The improvement is shown to be sharp as each new term of the series is added.

In this paper, we shall give an extension of operator Bellman inequality. This result is estimated via Kantorovich constant.

We present inequalities and some applications to Kellers' limit and Carlemans' inequality.

In this paper we establish improved Hardy and Rellich type inequalities on Riemannian manifold $M$. Furthermore, we also obtain sharp constant for the improved Hardy inequality and explicit constant for the Rellich inequality on hyperbolic…

We give a strengthening of the classical Khintchine inequality between the second and the $p$-th moment for $p \ge 3$ with optimal constant by adding a deficit depending on the vector of coefficients of the Rademacher sum.

The aim of this paper is to establish new inequalities for the Euler-Mascheroni by the continued fraction method.

We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.

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

In this paper we study some improvements of the classical Hardy inequality. We add to the right hand side of the inequality a term which depends on some Lorentz norms of $u$ or of its gradient and we find the best values of the constants…

In this short note, we give the refined Young inequality with Specht's ratio by only elementary and direct calculations. The obtained inequality is better than one previously shown by the author in 2012. In addition, we give a new property…

We compute the best constant in the Khintchine inequality under assumption that the sum of Rademacher random variables is zero.

We obtain simple proofs of certain inequalites for bivariate means.

We investigate the growth of the constants of the polynomial Hardy-Littlewood inequality.

In this paper we obtain a new constant in the P\'{o}lya-Vinogradov inequality. Our argument follows previously established techniques which use the Fourier expansion of an interval to reduce to Gauss sums. Our improvement comes from…

Some improvements of Young inequality and its reverse for positive numbers with Kontrovich constant are given. Using these inequalities some operator versions and Hilbert-Schmidt norm versions for matrices are proved.

We prove a one-dimensional Hardy inequality on the halfline with sharp constant, which improves the classical form of this inequality. As a consequence of this new inequality we can rederive known doubly weighted Hardy inequalities. Our…

We consider the Sobolev norms of the pointwise product of two functions, and estimate from above and below the constants appearing in two related inequalities.