We characterize the good weights for a certain weighted weak-type iterated Hardy inequality to hold. As consequence, we get characterizations of some bilinear inequalities.

Considerable attention has been given to Hilbert inequalities and Hilbert-type inequalities and their various generalizations by several authors including Handley et al. 1 , Minzhe and Bicheng 2 , Minzhe 3 , Hu 4 , Jichang 5 , Bicheng 6 , and Zhao 7, 8 . In 1998, Pachpatte 9 gave some new integral inequalities similar to Hilbert inequality see 10, page 226 . In 2000, Zhao and Debnath 11 establi...

for every u∈W1,p(Rn). It is easy to see that the proposition fails when s > 1, where s = q/p. In this paper we are trying to find out what happens if s > 1. We show that it does not only become true but obtains better estimates. The described result is stated and proved in Section 3. The method invoked is different from that by Cazenave in [2]; it relies on some Littlewood-Paley theory and Beso...

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 lower bound of 1 √ 2 in the complex Gaussian case and for the sequence of functions {en}n=1 . The second case is Junge’s recent Khintchine-type inequality for...

Abstract The aim of this work is to obtain quantum estimates for q -Hardy type integral inequalities on calculus. For this, we establish new identities including derivatives and numbers. After that, prove a generalized -Minkowski inequality. Finally, with the help obtained equalities inequality, results want. outcomes presented in paper are -extensions -generalizations comparable literature ine...

In the present article, we prove some new generalizations of dynamic inequalities Hardy-type by utilizing diamond-? integrals on time scales. Furthermore, in two variables scales are proved. Moreover, Hardy for several functions using The results proved Jensen inequality and Fubini theorem Our main extend existing integral discrete inequalities. Symmetry plays an essential role determining corr...