The vector-valued non-homogeneous Tb theorem

Details The vector-valued non-homogeneous Tb theorem The vector-valued non-homogeneous Tb theorem

2008-09-18

arxiv.org/abs/0809.3097v3

Mathematics

Functional Analysis

Substantial revision with stronger forms of the main theorems. 44 pages

Scientific paper

The paper gives a Banach space -valued extension of the Tb theorem of Nazarov, Treil and Volberg (2003) concerning the boundedness of singular integral operators with respect to a measure, which only satisfies an upper control on the size of balls. Under the same assumptions as in their result, such operators are shown to be bounded on the Bochner spaces of functions with values in a Banach space with the unconditionality property of martingale differences (UMD). The new proof deals directly with all Lebesgue exponents p in the range 1

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