English

Multilinear Embedding -- convolution estimates on smooth submanifolds

Analysis of PDEs 2012-04-26 v1

Abstract

Multilinear embedding estimates for the fractional Laplacian are obtained in terms of functionals defined over a hyperbolic surface. Convolution estimates used in the proof enlarge the classical framework of the convolution algebra for Riesz potentials to include the critical endpoint index, and provide new realizations for fractional integral inequalities that incorporate restriction to smooth submanifolds. Results developed here are modeled on the space-time estimate used by Klainerman and Machedon in their proof of uniqueness for the Gross-Pitaevskii hierarchy.

Keywords

Cite

@article{arxiv.1204.5684,
  title  = {Multilinear Embedding -- convolution estimates on smooth submanifolds},
  author = {William Beckner},
  journal= {arXiv preprint arXiv:1204.5684},
  year   = {2012}
}

Comments

11 pages, AMSLaTeX

R2 v1 2026-06-21T20:54:39.470Z