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arXiv · 1201.0648

The local non-homogeneous Tb theorem for vector-valued functions

Tuomas P. Hytönen·Antti V. Vähäkangas
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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.

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Tuomas P. Hytönen, Antti V. Vähäkangas. 2012-01-03. The local non-homogeneous Tb theorem for vector-valued functions. https://arxiv.org/abs/1201.0648

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