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

Studia Mathematica (2007)

- Volume: 182, Issue: 2, page 99-111
- ISSN: 0039-3223

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topSandra Pot. "A sufficient condition for the boundedness of operator-weighted martingale transforms and Hilbert transform." Studia Mathematica 182.2 (2007): 99-111. <http://eudml.org/doc/284477>.

@article{SandraPot2007,

abstract = {Let W be an operator weight taking values almost everywhere in the bounded positive invertible linear operators on a separable Hilbert space . We show that if W and its inverse $W^\{-1\}$ both satisfy a matrix reverse Hölder property introduced by Christ and Goldberg, then the weighted Hilbert transform $H:L²_\{W\}(ℝ, ) → L²_\{W\}(ℝ, )$ and also all weighted dyadic martingale transforms $T_\{σ\}: L²_\{W\}(ℝ, ) → L²_\{W\}(ℝ, )$ are bounded.
We also show that this condition is not necessary for the boundedness of the weighted Hilbert transform.},

author = {Sandra Pot},

journal = {Studia Mathematica},

keywords = {operator weight; dyadic martingale transform; weighted Hilbert transform; reverse Hölder property; weighted square function},

language = {eng},

number = {2},

pages = {99-111},

title = {A sufficient condition for the boundedness of operator-weighted martingale transforms and Hilbert transform},

url = {http://eudml.org/doc/284477},

volume = {182},

year = {2007},

}

TY - JOUR

AU - Sandra Pot

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

JO - Studia Mathematica

PY - 2007

VL - 182

IS - 2

SP - 99

EP - 111

AB - Let W be an operator weight taking values almost everywhere in the bounded positive invertible linear operators on a separable Hilbert space . We show that if W and its inverse $W^{-1}$ both satisfy a matrix reverse Hölder property introduced by Christ and Goldberg, then the weighted Hilbert transform $H:L²_{W}(ℝ, ) → L²_{W}(ℝ, )$ and also all weighted dyadic martingale transforms $T_{σ}: L²_{W}(ℝ, ) → L²_{W}(ℝ, )$ are bounded.
We also show that this condition is not necessary for the boundedness of the weighted Hilbert transform.

LA - eng

KW - operator weight; dyadic martingale transform; weighted Hilbert transform; reverse Hölder property; weighted square function

UR - http://eudml.org/doc/284477

ER -

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