English

Near equality in the Riesz-Sobolev inequality in higher dimensions

Classical Analysis and ODEs 2015-06-02 v1

Abstract

The Riesz-Sobolev inequality provides an upper bound for a trilinear expression involving convolution of indicator functions of sets. It is known that equality holds only for homothetic ordered triples of appropriately situated ellipsoids. We characterize ordered triples of subsets of Euclidean space RdR^d that nearly realize equality, for arbitrary dimensions dd, extending a result already known for d=1d=1.

Keywords

Cite

@article{arxiv.1506.00157,
  title  = {Near equality in the Riesz-Sobolev inequality in higher dimensions},
  author = {Michael Christ},
  journal= {arXiv preprint arXiv:1506.00157},
  year   = {2015}
}