Improved Hardy-Sobolev inequalities
Spectral Theory
2007-10-23 v1 Mathematical Physics
math.MP
Abstract
The main result includes features of a Hardy-type inequality and an inequality of either Sobolev or Gagliardo-Nirenberg type. It is inspired by the method of proof of a recent improved Sobolev inequality derived by M. Ledoux which brings out the connection between Sobolev embeddings and heat kernel bounds. Here Ledoux's technique is applied to the operator and the analysis requires the determination of the operator semigroup and its properties.
Cite
@article{arxiv.0710.3936,
title = {Improved Hardy-Sobolev inequalities},
author = {A. Balinsky and W. D. Evans and D. Hundertmark and R. T. Lewis},
journal= {arXiv preprint arXiv:0710.3936},
year = {2007}
}