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
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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, $q \neq p$.References
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Additional Information
- G. Barbatis
- Affiliation: Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
- MR Author ID: 602865
- Email: gbarbati@cc.uoi.gr
- S. Filippas
- Affiliation: Department of Applied Mathematics, University of Crete, 71409 Heraklion, Greece
- Email: filippas@tem.uoc.gr
- A. Tertikas
- Affiliation: Department of Mathematics, University of Crete, 71409 Heraklion, Greece and Institute of Applied and Computational Mathematics, FORTH, 71110 Heraklion, Greece
- Email: tertikas@math.uoc.gr
- Received by editor(s): February 28, 2001
- Published electronically: December 9, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 356 (2004), 2169-2196
- MSC (2000): Primary 35J20, 26D10; Secondary 46E35, 35Pxx
- DOI: https://doi.org/10.1090/S0002-9947-03-03389-0
- MathSciNet review: 2048514