Towards a unified theory of Sobolev inequalities

Joaquim Martin; Mario Milman

Towards a unified theory of Sobolev inequalities

Functional Analysis 2014-04-17 v3

Authors: Joaquim Martin , Mario Milman

Abstract

We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities. In particular, we discuss our recent papers on fractional order inequalities, Coulhon type inequalities, transference and dimensionless inequalities and our forthcoming work on sharp higher order Sobolev inequalities that can be obtained by iteration.

Keywords

Sobolev inequalities pointwise inequalities gradient isoperimetric profile fractional order inequalities Coulhon type inequalities sharp higher order inequalities

Cite

@article{arxiv.1311.6191,
  title  = {Towards a unified theory of Sobolev inequalities},
  author = {Joaquim Martin and Mario Milman},
  journal= {arXiv preprint arXiv:1311.6191},
  year   = {2014}
}

Comments

39 pages, made some changes to section 11

Towards a unified theory of Sobolev inequalities

Abstract

Keywords

Cite

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