$L^1$ Hardy inequalities with weights

created by psaradakis on 20 Feb 2017

[BibTeX]

Published Paper

Inserted: 20 feb 2017
Last Updated: 20 feb 2017

Journal: J. Geom. Anal.
Year: 2013

Abstract:

We prove sharp homogeneous improvements to $L^1$ weighted Hardy inequalities involving distance from the boundary. In the case of a smooth domain, we obtain lower and upper estimates for the best constant of the remainder term. These estimates are sharp in the sense that they coincide when the domain is a ball or an infinite strip. In the case of a ball, we also obtain further improvements.