Abstract We study weighted inequalities of Hardy and Hardy–Poincaré type find necessary sufficient conditions on the weights so that considered hold. Examples with optimal constants are shown. Such then used to quantify convergence rate solutions doubly nonlinear fast diffusion equation towards Barenblatt profile.

In this paper, we consider the [Formula: see text]-Hardy inequalities on the sphere. By the divergence theorem, we establish the [Formula: see text]-Hardy inequalities on the sphere. Furthermore, we also obtain their best constants. Our results can be regarded as the extension of Xiao's (J. Math. Inequal. 10:793-805, 2016).

In 2012, W. T. Sulaiman presented new kinds of Hardy’s integral inequalities. In this paper, we derive some new extensions of the famous Hardy’s integral inequality. The results present direct generalization of the original Hardy inequality. In addition, the corresponding reverse relation is also obtained.

k=1 |ak|, in which C = (cj,k) and the parameter p are assumed fixed (p > 1), and the estimate is to hold for all complex sequences a. The lp operator norm of C is then defined as the p-th root of the smallest value of the constant U : ||C||p,p = U 1 p . Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cj,k = 1/j, k ≤ j and 0 otherwise, is bounded on lp and has norm ≤ ...

We consider the fractional Laplacian with Hardy potential and study scale of homogeneous $L^p$ Sobolev spaces generated by this operator. Besides generalized reversed inequalities, analysis relies on a H\"ormander multiplier theorem which is crucial to construct basic Littlewood--Paley theory. The results extend those obtained recently in $L^2$ but do not cover negative coupling constants gener...

We prove a natural generalization of Kneser's oscillation criterion and Hardy's inequality for Sturm{Liouville diierential expressions. In particular, assuming ? d dx p 0 (x) d dx + q 0 (x), x 2 (a; b), ?1 a < b 1 to be nonoscillatory near a (or b), we determine conditions on q(x) such that ? d dx p 0 (x) d dx + q 0 (x) + q(x) is nonoscillatory, respectively, oscillatory near a (or b).

Résumé Dans cet article, on étudie les fonctions maximales de Hardy–Littlewood pour une grande famille de mesures sur les variétés cuspidales. En particulier, on étudie une famille de variétés à croissance exponentielle du volume sur lesquelles la fonction maximale centrée de Hardy–Littlewood est de type faible (1,1), et la fonction maximale non-centrée de Hardy–Littlewood est bornée sur Lp pou...