Recovering singular integrals from Haar shifts

DOI10.1090/S0002-9939-2010-10426-4zbMath1207.42013arXiv0911.4968MaRDI QIDQ3065709

Armen Vagharshakyan

Publication date: 6 January 2011

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

Full work available at URL: https://arxiv.org/abs/0911.4968

zbMATH Keywords

Calderón-Zygmund operatorsweighted estimates

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Multipliers in one variable harmonic analysis (42A45)

Related Items (13)

Representation of singular integrals by dyadic operators, and the \(A_2\) theorem ⋮ Mixed \(A_p\)-\(A_r\) inequalities for classical singular integrals and Littlewood-Paley operators ⋮ Sharp logarithmic estimates for positive dyadic shifts ⋮ Wavelet representation of singular integral operators ⋮ The sharp weighted maximal inequalities for noncommutative martingales ⋮ Sharp weighted norm inequalities for Littlewood-Paley operators and singular integrals ⋮ The sharp weighted bound for general Calderón-Zygmund operators ⋮ Burkholder’s function and a weighted 𝐿² bound for stochastic integrals ⋮ A weak-\(L^\infty\) inequality for weakly dominated martingales with applications to Haar shift operators ⋮ Sharp weighted estimates for classical operators ⋮ A simple proof of the sharp weighted estimate for Calderón-Zygmund operators on homogeneous spaces ⋮ Sharp weak-type \((p,p)\) estimates \((1<p<\infty)\) for positive dyadic shifts ⋮ An abstract theory of singular operators

Cites Work

• Unnamed Item
• Two weight inequalities for individual Haar multipliers and other well localized operators
• On Petermichl's dyadic shift and the Hilbert transform
• Sharp \(A_{2}\) inequality for Haar shift operators
• \(A_1\) bounds for Calderón-Zygmund operators related to a problem of Muckenhoupt and Wheeden
• Sharp estimate of the Ahlfors-Beurling operator via averaging martingale transforms
• Why the Riesz transforms are averages of the dyadic shifts?
• The \(Tb\)-theorem on non-homogeneous spaces.
• Iterated Riesz Commutators: A Simple Proof of Boundedness
• Multiparameter Riesz commutators
• The Bellman functions and two-weight inequalities for Haar multipliers
• 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
• The sharp weighted bound for the Riesz transforms

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