English

On the Separated Bumps Conjecture for Calderon-Zygmund Operators

Classical Analysis and ODEs 2014-03-20 v4

Abstract

We study the `separated bump conjecture' of Cruz-Uribe & Perez, and Cruz-Uribe & Reznikov & Volberg. In the L^p setting, we formulate a stronger version of this conjecture, and show that under it, a two weight inequality holds for all CZOs. When p=2, this is the result of Nazarov & Reznikov & Volberg (1306.2653). Our argument is based on stopping time arguments and the extra hypothesis is used in a clear-cut and seemingly essential way. This argument could be of some help in searching for a counterexample to the conjecture.

Keywords

Cite

@article{arxiv.1310.3507,
  title  = {On the Separated Bumps Conjecture for Calderon-Zygmund Operators},
  author = {Michael T Lacey},
  journal= {arXiv preprint arXiv:1310.3507},
  year   = {2014}
}

Comments

15 pages. v4: to appear in Hokkaido Math J