On Petermichl's dyadic shift and the Hilbert transform

DOI10.1016/j.crma.2008.09.021zbMath1151.42004OpenAlexW1999553762MaRDI QIDQ957551

Tuomas P. Hytönen

Publication date: 28 November 2008

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2008.09.021

Mathematics Subject Classification ID

Conjugate functions, conjugate series, singular integrals (42A50) Probabilistic methods for one variable harmonic analysis (42A61)

Related Items (14)

Commutators with fractional integral operators ⋮ Logarithmic mean oscillation on the polydisc, endpoint results for multi-parameter paraproducts, and commutators on BMO ⋮ Lower bounds for the Dyadic Hilbert transform ⋮ Local \( Tb \) theorems and Hardy inequalities ⋮ A weighted maximal inequality for differentially subordinate martingales ⋮ The Two Weight Inequality for the Hilbert Transform: A Primer ⋮ A Two Weight Fractional Singular Integral Theorem with Side Conditions, Energy and k-Energy Dispersed ⋮ A two weight inequality for the Hilbert transform assuming an energy hypothesis ⋮ Dyadic Harmonic Analysis and Weighted Inequalities: The Sparse Revolution ⋮ The two weight \(T1\) theorem for fractional Riesz transforms when one measure is supported on a curve ⋮ Logarithmic mean oscillation on the polydisc, multi-parameter paraproducts and iterated commutators ⋮ A two weight local \(Tb\) theorem for the Hilbert transform ⋮ Recovering singular integrals from Haar shifts ⋮ Recent developments in two weight testing theory

Cites Work

• The \(Tb\)-theorem on non-homogeneous spaces.
• A version of Burkholder’s theorem for operator-weighted spaces
• Dyadic shifts and a logarithmic estimate for Hankel operators with matrix symbol
• The sharp bound for the Hilbert transform on weighted Lebesgue spaces in terms of the classical A p characteristic
• Unnamed Item

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