English

A local Tb theorem for matrix weighted paraproducts

Classical Analysis and ODEs 2014-11-14 v1 Analysis of PDEs

Abstract

We prove a local TbTb theorem for paraproducts acting on vector valued functions, with matrix weighted averaging operators. The condition on the weight is that its square is in the L2L_2 associated matrix AA_\infty class. We also introduce and use a new matrix reverse H\"older class. This result generalizes the previously known case of scalar weights from the proof of the Kato square root problem, as well as the case of diagonal weights, recently used in the study of boundary value problems for degenerate elliptic equations.

Keywords

Cite

@article{arxiv.1411.3376,
  title  = {A local Tb theorem for matrix weighted paraproducts},
  author = {Andreas Rosén},
  journal= {arXiv preprint arXiv:1411.3376},
  year   = {2014}
}
R2 v1 2026-06-22T06:57:01.035Z