An example is given of an operator weight W that satisfies the dyadic operator Hunt–Muckenhoupt–Wheeden condition [Aopf ] d 2 for which there exists a dyadic martingale transform on L 2 ( W ) that is unbounded. The construction relates weighted boundedness to the boundedness of dyadic vector Hankel operators.
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Gillespie et al. (2001) studied this question.
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