Extensions of Hiai-Lin type eigenvalue inequality

Some new extensions of Hardy`s inequality

In this study, by a non-negative homogeneous kernel k we prove some extensions of Hardy's inequalityin two and three dimensions

Hilbert’s Type Linear Operator and Some Extensions of Hilbert’s Inequality

Extensions of Hardy Inequality

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...

On some nonlinear extensions of the Gagliardo-Nirenberg inequality with applications to nonlinear eigenvalue problems

We derive inequality ∫ R |f ′(x)|ph(f(x))dx ≤ (√ p− 1 )p ∫ R (√ |f ′′(x)Th(f(x))| )p h(f(x))dx, where f belongs locally to Sobolev space W 2,1 and f ′ has bounded support. Here h(·) is a given function and Th(·) is its given transform, it is independent of p. In case when h ≡ 1 we retrieve the well known inequality: ∫ R |f ′(x)|pdx ≤ (√ p− 1 )p ∫ R (√ |f (x)f(x)| )p dx. Our inequalities have fo...

Operator Extensions of Hua’s Inequality

Abstract. We give an extension of Hua’s inequality in pre-Hilbert C∗-modules without using convexity or the classical Hua’s inequality. As a consequence, some known and new generalizations of this inequality are deduced. Providing a Jensen inequality in the content of Hilbert C∗-modules, another extension of Hua’s inequality is obtained. We also present an operator Hua’s inequality, which is eq...