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arXiv · 1204.6526

The Perfect Local $ Tb$ Theorem and Twisted Martingale Transforms

Michael T. Lacey·Antti V. Vähäkangas
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Abstract

A local Tb Theorem provides a flexible framework for proving the boundedness of a Calder\'on-Zygmund operator T. One needs only boundedness of the operator T on systems of locally pseudo-accretive functions \{b_Q\}, indexed by cubes. We give a new proof of this Theorem in the setting of perfect (dyadic) models of Calder\'on-Zygmund operators, imposing integrability conditions on the b_Q functions that are the weakest possible. The proof is a simple direct argument, based upon a new inequality for transforms of so-called twisted martingale differences.

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BibTeXRIS

Michael T. Lacey, Antti V. Vähäkangas. 2012-04-29. The Perfect Local $ Tb$ Theorem and Twisted Martingale Transforms. https://doi.org/10.1090/s0002-9939-2014-11930-7

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