A unified approach to improved Lp hardy inequalities with best constants

We present a unified approach to improved L-p Hardy inequalities in R-N. We consider Hardy potentials that involve either the distance from a point, or the distance from the boundary, or even the intermediate case where the distance is taken from a surface of codimension 1 < k < N. In our main result, we add to the right hand side of the classical Hardy inequality a weighted L-p norm with optimal weight and best constant. We also prove non-homogeneous improved Hardy inequalities, where the right hand side involves weighted L-q norms, q not equal p.