A local theorem for matrix weighted paraproducts
Andreas Rosén
Chalmers University of Technology, Gothenburg, Sweden
![A local $Tb$ theorem for matrix weighted paraproducts cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rmi-volume-32-issue-4.png&w=3840&q=90)
Abstract
We prove a local 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 associated matrix class. We also introduce and use a new matrix reverse Hölder 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.
Cite this article
Andreas Rosén, A local theorem for matrix weighted paraproducts. Rev. Mat. Iberoam. 32 (2016), no. 4, pp. 1259–1276
DOI 10.4171/RMI/915