English

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.

Keywords

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