Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

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

100%

Pot S.

Studia Mathematica

2007

tom 182

nr 2

99-111

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 $W^{-1}$ both satisfy a matrix reverse Hölder property introduced by Christ and Goldberg, then the weighted Hilbert transform $H:L²_{W}(ℝ,𝓗 ) → L²_{W}(ℝ,𝓗 )$ and also all weighted dyadic martingale transforms $T_{σ}: L²_{W}(ℝ,𝓗 ) → L²_{W}(ℝ,𝓗 )$ are bounded. We also show that this condition is not necessary for the boundedness of the weighted Hilbert transform.

Ograniczanie wyników

1 Studia Mathematica

1 Pot S.

1 2007

Wyniki wyszukiwania

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