A two weight theorem for fractional singular integrals with an energy side condition and quasicube testing
Classical Analysis and ODEs
2015-05-26 v9
Abstract
We prove a two weight theorem for fractional singular integrals in higher dimensions assuming energy side conditions on the weights. The testing conditions are taken over quasicubes, namely globally biLipschitz images of cubes.
Cite
@article{arxiv.1302.5093,
title = {A two weight theorem for fractional singular integrals with an energy side condition and quasicube testing},
author = {Eric T. Sawyer and Chun-Yen Shen and Ignacio Uriarte-Tuero},
journal= {arXiv preprint arXiv:1302.5093},
year = {2015}
}
Comments
100 pages. This version corrects more typos, and clarifies arguments, especially in proving functional energy from energy. We also extend the testing conditions to quasicubes, a largely cosmetic exercise, but providing more flexibility in applications. We thank Michael Lacey for alerting us to several problems and omissions in earlier versions of this paper