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A unified approach to improved L^p Hardy inequalities with best constants

G. Barbatis·S. Filippas·A. Tertikas
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Abstract

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 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 \neq p.

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G. Barbatis, S. Filippas, A. Tertikas. 2003-02-26. A unified approach to improved L^p Hardy inequalities with best constants. https://arxiv.org/abs/math/0302326

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