English

A two weight local $Tb$ theorem for $n$-dimensional fractional singular integrals

Classical Analysis and ODEs 2020-11-12 v1

Abstract

We obtain a local two weight TbTb theorem with an energy side condition for higher dimensional fractional Calder\'{o}n-Zygmund operators. The proof follows the general outline of the proof for the corresponding one-dimensional TbTb theorem in [SaShUr12], but encountering a number of new challenges, including several arising from the failure in higher dimensions of T. Hyt\"{o}nen's one-dimensional two weight A2A_{2} inequality [Hyt].

Keywords

Cite

@article{arxiv.2011.05637,
  title  = {A two weight local $Tb$ theorem for $n$-dimensional fractional singular integrals},
  author = {Christos Grigoriadis and Michail Paparizos and Eric T. Sawyer and Chun-Yen Shen and Ignacio Uriarte-Tuero},
  journal= {arXiv preprint arXiv:2011.05637},
  year   = {2020}
}

Comments

arXiv admin note: text overlap with arXiv:1709.09595

R2 v1 2026-06-23T20:04:33.525Z