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

Barbatis, G.; Filippas, S.; Tertikas, A.

doi:10.1090/S0002-9947-03-03389-0

A unified approach to improved $L^p$ Hardy inequalities with best constants
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by G. Barbatis, S. Filippas and A. Tertikas PDF

Trans. Amer. Math. Soc. 356 (2004), 2169-2196 Request permission

Abstract:

We present a unified approach to improved $L^p$ Hardy inequalities in $\mathbf {R}^N$. 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 nonhomogeneous improved Hardy inequalities, where the right hand side involves weighted $L^q$ norms, $q \neq p$.

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