A Hardy Goldfish

A new restructured Hardy-Littlewood's inequality

In this paper, we reconstruct the Hardy-Littlewood’s inequality byusing the method of the weight coefficient and the technic of real analysis includinga best constant factor. An open problem is raised.

A Hardy–Moser–Trudinger inequality

In this paper we obtain an inequality on the unit disk B in R2, which improves the classical Moser-Trudinger inequality and the classical Hardy inequality at the same time. Namely, there exists a constant C0 > 0 such that ∫ B e 4πu2 H(u) dx ≤ C0 <∞, ∀ u ∈ C 0 (B), where H(u) := ∫

A Review of Hardy Inequalities

We review the literature concerning the Hardy inequality for regions in Euclidean space and in manifolds, concentrating on the best constants. We also give applications of these inequalities to boundary decay and spectral approximation. AMS subject classifications: 35P99, 35P20, 47A75, 47B25 keywords: Hardy inequality, boundary decay, Laplacian, elliptic operators, spectral theory, eigenfunctio...

A Hardy-Hilbert Type Inequality

On a decomposition of Hardy--Hilbert's type inequality

In this paper, two pairs of new inequalities are given, which decompose two Hilbert-type inequalities.