On general local $Tb$ theorems

DOI10.1090/S0002-9947-2012-05599-1zbMath1279.42013arXiv1011.0642OpenAlexW2907463012MaRDI QIDQ2841372

Henri Martikainen, Tuomas P. Hytönen

Publication date: 25 July 2013

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.0642

zbMATH Keywords

doubling measureCalderón-Zygmund operatornon-homogeneous spacemartingale square function

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25)

Related Items (16)

𝐿^{𝑝}-square function estimates on spaces of homogeneous type and on uniformly rectifiable sets ⋮ Two‐weight Tb theorems for well‐localized operators ⋮ Local \(Tb\) theorem with \(L^2\) testing conditions and general measures: square functions ⋮ Some characterizations of upper doubling conditions on metric measure spaces ⋮ GENERALIZED LOCAL THEOREMS FOR SQUARE FUNCTIONS ⋮ A Good-λ Lemma, Two Weight T1 Theorems Without Weak Boundedness, and a Two Weight Accretive Global Tb Theorem ⋮ A local \(Tb\) theorem for square functions in domains with Ahlfors-David regular boundaries ⋮ A two weight inequality for Calderón-Zygmund operators on spaces of homogeneous type with applications ⋮ The perfect local $Tb$ Theorem and twisted Martingale transforms ⋮ A non-homogeneous local Tb theorem for Littlewood-Paley \(g^*_{\lambda}\)-function with \(L^{p}\)-testing condition ⋮ On the Local Tb Theorem: A Direct Proof under the Duality Assumption ⋮ A two weight local \(Tb\) theorem for the Hilbert transform ⋮ Comparison of $T1$ conditions for multi-parameter operators ⋮ Littlewood-Paley theory on metric spaces with non doubling measures and its applications ⋮ The local \(Tb\) theorem with rough test functions ⋮ Boundedness and applications of singular integrals and square functions: a survey

Cites Work

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• The sharp weighted bound for general Calderón-Zygmund operators
• Local Tb theorem on spaces of homogeneous type
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• BCR algorithm and the \(T(b)\) theorem
• Vector-valued non-homogeneous \(Tb\) theorem on metric measure spaces
• Accretive system \(Tb\)-theorems on nonhomogeneous spaces.
• Carleson measures, trees, extrapolation, and \(T(b)\) theorems
• The \(Tb\)-theorem on non-homogeneous spaces.
• Non-homogeneous \(Tb\) theorem and random dyadic cubes on metric measure spaces
• Local \( Tb \) theorems and Hardy inequalities
• The vector-valued nonhomogeneous Tb Theorem
• The Hardy space H¹ on non-homogeneous metric spaces
• A T(b) theorem with remarks on analytic capacity and the Cauchy integral

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