We investigate the growth of the constants of the polynomial Hardy-Littlewood inequality.

This study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real function u x and a parameter λ. In particular, some sharp results of the classical Hilbert inequality are obtained by means of a sharpening of the Cauchy inequality. As applications, some refinements of both the Fejer-Riesz inequality and Hardy inequality inHp function are given.

This study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real function u x and a parameter λ. In particular, some sharp results of the classical Hilbert inequality are obtained by means of a sharpening of the Cauchy inequality. As applications, some refinements of both the Fejer-Riesz inequality and Hardy inequality inHp function are given.

We give a short and unified proof of Hardy-Lieb-Thirring inequalities for moments of eigenvalues of fractional Schrödinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, Sørensen, and Spitzer. Moreover, we prove that any non-magnetic Lieb-Thirring inequality implies a magnetic Lieb-Thirring inequality (with possibly a larger constant).

Inequalities of the form ∑∞ k=0 |f̂(mk)| k+1 ≤ C ‖f‖1 for all f ∈ H1, where {mk} are special subsequences of natural numbers, are investigated in the vector-valued setting. It is proved that Hardy’s inequality and the generalized Hardy inequality are equivalent for vector valued Hardy spaces defined in terms of atoms and that they actually characterize B-convexity. It is also shown that for 1 < ...

(1.1) and (1.2) is the well known Hardy-Littlewood-Polya’s inequality. In connection with applications in analysis, their generalizations and variants have received considerable interest recent years. Firstly, by means of introducing a parameter, two forms of extended Hardy-Littlewood-Polya’s inequality are obtained by Hu in [2] as follows. (1) Let λ > 0, p > 1, 1 p+ 1 q=1, f(x), g(y) ≥ 0, F (x...

In 1986 A. Ancona showed, using the Koebe one-quarter Theorem, that for a simply-connected planar domain the constant in the Hardy inequality with the distance to the boundary is greater than or equal to 1/16. In this paper we consider classes of domains for which there is a stronger version of the Koebe Theorem. This implies better estimates for the constant appearing in the Hardy inequality. ...

We give a new, simpler proof of the fractional Korn's inequality for subsets $\mathbb{R}^d$. also show framework obtaining directly from appropriate Hardy-type inequality.

In this paper, we study Hardy–Sobolev inequalities on hypersurfaces of [Formula: see text], all them involving a mean curvature term and having universal constants independent the hypersurface. We first consider celebrated Sobolev inequality Michael–Simon Allard, in our codimension one framework. Using their ideas, but simplifying presentations, give quick easy-to-read proof inequality. Next, e...