The local non-homogeneous Tb theorem for vector-valued functions
Functional Analysis
2012-01-04 v1
Abstract
We extend the local non-homogeneous Tb theorem of Nazarov, Treil and Volberg to the setting of singular integrals with operator-valued kernel that act on vector-valued functions. Here, `vector-valued' means `taking values in a function lattice with the UMD (unconditional martingale differences) property'. A similar extension (but for general UMD spaces rather than UMD lattices) of Nazarov-Treil-Volberg's global non-homogeneous Tb theorem was achieved earlier by the first author, and it has found applications in the work of Mayboroda and Volberg on square-functions and rectifiability. Our local version requires several elaborations of the previous techniques, and raises new questions about the limits of the vector-valued theory.
Cite
@article{arxiv.1201.0648,
title = {The local non-homogeneous Tb theorem for vector-valued functions},
author = {Tuomas P. Hytönen and Antti V. Vähäkangas},
journal= {arXiv preprint arXiv:1201.0648},
year = {2012}
}