Location of Repository

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) → L<sup>2</sup><sub>W</sub>(R,H) and also all weighted dyadic martingale transforms T<sub>σ</sub>: L<sup>2</sup><sub>W</sub>(R,H) → 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

Publisher: Polska Akademia Nauk

Year: 2007

OAI identifier:
oai:eprints.gla.ac.uk:13047

Provided by:
Enlighten

Downloaded from
http://eprints.gla.ac.uk/13047/1/id13047.pdf

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

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.