A unified approach to improved  Hardy inequalities with best constants |
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| Authors: | G Barbatis S Filippas A Tertikas |
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| Institution: | Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece ; Department of Applied Mathematics, University of Crete, 71409 Heraklion, Greece ; Department of Mathematics, University of Crete, 71409 Heraklion, Greece and Institute of Applied and Computational Mathematics, FORTH, 71110 Heraklion, Greece |
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| Abstract: | We present a unified approach to improved  Hardy inequalities in  . 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  . In our main result, we add to the right hand side of the classical Hardy inequality a weighted  norm with optimal weight and best constant. We also prove nonhomogeneous improved Hardy inequalities, where the right hand side involves weighted  norms,  . |
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| Keywords: | Hardy inequalities best constants distance function weighted norms |
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