THE LOCAL NON-HOMOGENEOUS Tb THEOREM FOR VECTOR-VALUED FUNCTIONS
2014 ◽
Vol 57
(1)
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pp. 17-82
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AbstractWe 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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2006 ◽
Vol 186
(3)
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pp. 455-468
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Keyword(s):
2017 ◽
Vol 173
(2)
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pp. 357-390
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2001 ◽
Vol 70
(3)
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pp. 323-336
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2019 ◽
Vol 472
(2)
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pp. 1293-1312
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1974 ◽
Vol 26
(4)
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pp. 841-853
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2013 ◽
Vol 193
(5)
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pp. 1397-1430
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