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

• Autorzy: Sandra Pot
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
• 42A61: Probabilistic methods
• 42A50: Conjugate functions, conjugate series, singular integrals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 182
• Numer: 2
• Strony: 99-111

Daty

wydano

2007

Twórcy

autor

Sandra Pot

• Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK

Identyfikatory

DOI

10.4064/sm182-2-1