Geodesic
THE LOCAL NON-HOMOGENEOUS Tb THEOREM FOR VECTOR-VALUED FUNCTIONS
Glasgow mathematical journal, Tome 57 (2015) no. 1, pp. 17-82

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DOI

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. 
HYTÖNEN, TUOMAS P.; VÄHÄKANGAS, ANTTI V. THE LOCAL NON-HOMOGENEOUS Tb THEOREM FOR VECTOR-VALUED FUNCTIONS. Glasgow mathematical journal, Tome 57 (2015) no. 1, pp. 17-82. doi: 10.1017/S0017089514000123
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     title = {THE {LOCAL} {NON-HOMOGENEOUS} {Tb} {THEOREM} {FOR} {VECTOR-VALUED} {FUNCTIONS}},
     journal = {Glasgow mathematical journal},
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     year = {2015},
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