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Journal of the London Mathematical Society 2001 64(3):624-636; doi:10.1112/S0024610701002599
© 2001 by London Mathematical Society
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© The London Mathematical Society

Logarithmic Growth for Matrix Martingale Transforms

T. A. Gillespie, S. Pott, S. Treil and A. Volberg

Department of Mathematics and Statistics, University of Edinburgh Edinburgh EH9 3JZ
Department of Mathematics, Michigan State University East Lansing, MI 48824, USA

Received 3 July 2000. Revision received 5 April 2001.

An example is given of an operator weight W that satisfies the dyadic operator Hunt–Muckenhoupt–Wheeden condition Formula for which there exists a dyadic martingale transform on L2 (W) that is unbounded. The construction relates weighted boundedness to the boundedness of dyadic vector Hankel operators.


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