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## A sufficient condition for the boundedness of operator-weighted martingale transforms and Hilbert transform

### Abstract

Let W be an operator weight taking values almost everywhere in the bounded positive invertible linear operators on a separable Hilbert space H. We show that if W and its inverse W<sup>−1</sup> both satisfy a matrix reverse Holder property introduced in [2], then the weighted Hilbert transform H :\ud L<sup>2</sup><sub>W</sub>(R,H) &#8594; L<sup>2</sup><sub>W</sub>(R,H) and also all weighted dyadic martingale transforms T<sub>&#963;</sub>: L<sup>2</sup><sub>W</sub>(R,H) &#8594; L<sup>2</sup><sub>W</sub>(R,H) are bounded.\ud We also show that this condition is not necessary for the boundedness of the weighted Hilbert transform

Topics: QA
Year: 2007
OAI identifier: oai:eprints.gla.ac.uk:13047
Provided by: Enlighten

### Citations

1. (2003). A version of Burkholder’s Theorem for operator-weighted L2-spaces, to appear in
2. Hardy spaces of vector-valued functions:duality,
3. Lecture Notes on Dyadic Harmonic Analysis,
4. Logarithmic growth for matrix martingale transforms,
5. Logarithmic growth for weighted Hilbert transform and vector Hankel operators, to appear in
6. Matrix Ap weights via S-functions,
7. Matrix BMO and matrix A2 weights: A substitute for the classical exp-relationship,
8. The hunt for a Bellman function: applications to estimates for singular integral operators and to other classical problems of harmonic analysis,
9. (2001). The transfer method in estimates for vector Hankel operators Algebra i Analiz12(2000),
10. (2001). Vector A2 weights and a Hardy-Littlewood maximal function,
11. Wavelets and the angle between past and future,
12. Weighted norm inequalities for the conjugate function and Hilbert transform,

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