A logarithmic Hardy inequality

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 more accurate half-discrete Hardy-Hilbert-type inequality with the logarithmic function

By means of the weight functions, the technique of real analysis and Hermite-Hadamard's inequality, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of logarithmic function and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions, the reverses and some particular cases are also considered.

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.