The proof of the nonhomogeneous $T1$ theorem via averaging of dyadic shifts

DOI10.1090/spmj/1395zbMath1335.42014arXiv1303.0367OpenAlexW2963881692MaRDI QIDQ2797729

Alexander Volberg

Publication date: 6 April 2016

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.0367

zbMATH Keywords

dyadic shifts\(T1\) theoremnondoubling measurenonhomogeneous Calderón-Zygmund operators

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20)

Cites Work

• Unnamed Item
• The sharp weighted bound for general Calderón-Zygmund operators
• Two weight inequalities for individual Haar multipliers and other well localized operators
• A boundedness criterion for generalized Calderón-Zygmund operators
• The \(Tb\)-theorem on non-homogeneous spaces.
• Non-homogeneous \(Tb\) theorem and random dyadic cubes on metric measure spaces
• \(L^2\)-boundedness of the Cauchy integral operator for continuous measures
• Sharp weighted estimates for dyadic shifts and the \(A_2\) conjecture
• A T(b) theorem with remarks on analytic capacity and the Cauchy integral
• The proof of $A_2$ conjecture in a geometrically doubling metric space

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