English

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 L:=xL:= {\bf{x}} \cdot \nabla and the analysis requires the determination of the operator semigroup {etLL}t>0\{e^{-tL^{*}L}\}_{t>0} and its properties.

Keywords

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}
}
R2 v1 2026-06-21T09:34:27.202Z