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