Related papers: On Some Double-Series Inequalities

We establish a family of parametric isoperimetric-type inequalities with multiple geometric quantities for closed convex curves. These inequalities hold under certain parameter conditions. We also prove the equality conditions. Some new…

Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial…

We improve the classical discrete Hardy inequality \begin{equation*}\label{1} \sum _{{n=1}}^{\infty }a_{n}^{2}\geq \left({\frac {1}{2}}\right)^{2} \sum _{{n=1}}^{\infty }\left({\frac {a_{1}+a_{2}+\cdots +a_{n}}{n}}\right)^{2},…

We study some Hardy-type inequalities involving a general norm in $R^n$ and an anisotropic distance function to the boundary. The case of the optimality of the constants is also addressed.

The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…

We establish a novel improvement of the classical discrete Hardy inequality, which gives the discrete version of a recent (continuous) inequality of Frank, Laptev, and Weidl. Our arguments build on certain weighted inequalities based on…

In this note we prove a weighted version of the Khintchine inequalities.

In this paper we provide a family of inequalities, extending a recent result due to Albuquerque et al.

Using double counting, we prove Delsarte inequalities for $q$-ary codes and their improvements. Applying the same technique to $q$-ary constant-weight codes, we obtain new inequalities for $q$-ary constant-weight codes.

We correct a mistake in the paper ["On weighted iterated Hardy-type inequalities", Positivity, 22 (1) (2018), 275-299]. -- In this paper the inequality $$ \bigg( \int_0^{\infty} \bigg( \int_x^{\infty} \bigg( \int_t^{\infty} h \bigg)^q…

This a very brief account of the main line of development of Hardy inequalities.

We prove a sharp integral inequality that generalizes the well known Hardy type integral inequality for negative exponents. We also give sharp applications in two directions for Muckenhoupt weights on R. This work refines the results that…

We extend the work of Dyda and Kijaczko by establishing the corresponding weighted fractional Hardy inequalities with singularities on any flat submanifolds. While they derived weighted fractional Hardy inequalities with singularities at a…

We prove a two dimensional Holder and reverse-Holder inequality on time scales via the diamond-alpha integral. Other integral inequalities are established as well, which have as corollaries some recent proved Hardy-type inequalities on time…

We establish in this paper some weighted Hardy and Rellich type inequalities on the half line in the framework of equalities, extending recent results proved by Machihara-Ozawa-Wadade and Bez-Machihara-Ozawa. In particular, the…

We study the Schr\"odinger-Robertson uncertainty relations in an algebraic framework. Moreover, we show that some specific commutation relations imply new equalities, which are regarded as equality versions of well-known inequalities such…

This paper is devoted to the study of sequences in overpartitions and their relation to 2-color partitions. An extensive study of a general class of double series is required to achieve these ends.

A result of Bennett and Grosse-Erdmann characterizes the weights for which the corresponding weighted Hardy inequality holds on the cone of non-negative, non-increasing sequences and a bound for the best constant is given. In this paper, we…

It is proved that, under certain restrictions on weights, a pair of weighted Hardy spaces on the two-dimensional torus is K-closed in the pair of the corresponding weighted Lebesgue spaces. By now, K-closedness of Hardy spaces on the…

We study the higher order q- Poincar\'e and other coercive inequalities for a class probability measures satisfying Adam's regularity condition.