English

On Hardy-Sobolev embedding

Analysis of PDEs 2009-07-24 v1

Abstract

Linear interpolation inequalities that combine Hardy's inequality with sharp Sobolev embedding are obtained using classical arguments of Hardy and Littlewood (Bliss lemma). Such results are equivalent to Caffarelli-Kohn-Nirenberg inequalities with sharp constants. A one-dimensional convolution inequality for the exponential density is derived as an application of these methods.

Keywords

Cite

@article{arxiv.0907.3932,
  title  = {On Hardy-Sobolev embedding},
  author = {William Beckner},
  journal= {arXiv preprint arXiv:0907.3932},
  year   = {2009}
}

Comments

7 pages, AMSLaTex

R2 v1 2026-06-21T13:27:57.770Z