English

Near-extremizers of Young's Inequality for R^d

Classical Analysis and ODEs 2011-12-22 v1

Abstract

If a pair of functions nearly extremizes Young's convolution inequality for R^d, with all three exponents finite and strictly greater than 1, then each function is close in norm to a Gaussian. The proof relies on the Riesz-Sobolev rearrangement inequality and in particular, on an approximate inverse Riesz-Sobolev inequality established in a companion paper.

Keywords

Cite

@article{arxiv.1112.4875,
  title  = {Near-extremizers of Young's Inequality for R^d},
  author = {Michael Christ},
  journal= {arXiv preprint arXiv:1112.4875},
  year   = {2011}
}