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LOGARITHMIC GROWTH FOR MATRIX MARTINGALE TRANSFORMS

Published online by Cambridge University Press:  30 January 2002

T. A. GILLESPIE ,
S. POTT ,
S. TREIL  and
A. VOLBERG
T. A. GILLESPIE
Affiliation:
Department of Mathematics and Statistics, University of Edinburgh, Edinburgh EH9 3JZ
S. POTT
Affiliation:
Department of Mathematics and Statistics, University of Edinburgh, Edinburgh EH9 3JZ
S. TREIL
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
A. VOLBERG
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
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Abstract

An example is given of an operator weight W that satisfies the dyadic operator Hunt–Muckenhoupt–Wheeden condition [Aopf ]d2 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.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 64 , Issue 3 , December 2001 , pp. 624 - 636
Copyright
London Mathematical Society 2001

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