We prove a new inequality which improves on the classical Hardy inequality in the sense that a nonlinear integral quantity with super-quadratic growth, which is computed with respect to an inverseâ€¦ (More)

We present a unified approach to improved Lp Hardy inequalities in R . We consider Hardy potentials that involve either the distance from a point, or the distance from the boundary, or even theâ€¦ (More)

We consider the problem of high-frequency asymptotics for the time-dependent onedimensional SchrÃ¶dinger equation with rapidly oscillating initial data. This problem is commonly studied via the WKBâ€¦ (More)

We obtain Sobolev inequalities for the ShcrÃ¶dinger operator âˆ’âˆ† âˆ’ V , where V has critical behaviour V (x) = ((N âˆ’ 2)/2)2|x|âˆ’2 near the origin. We apply these inequalities to obtain pointwiseâ€¦ (More)

Abstract In this article we establish new improvements of the optimal Hardy inequality in the half space. We first add all possible linear combinations of Hardy type terms thus revealing theâ€¦ (More)

We consider a general class of sharp L p Hardy inequalities in IR N involving distance from a surface of general codimension 1 â‰¤ k â‰¤ N. We show that we can succesively improve them by adding to theâ€¦ (More)