Sharp estimate of the Ahlfors-Beurling operator via averaging martingale transforms

DOI10.1307/mmj/1060013205zbMath1056.42011OpenAlexW1965326172MaRDI QIDQ1411316

Alexander Volberg, Oliver Dragičević

Publication date: 27 October 2003

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1307/mmj/1060013205

zbMATH Keywords

singular integralboundednessBeltrami equationAhlfors-Beurling operatortwo-dimensional martingale transform

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Integral operators (47G10)

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Sharp bounds for general commutators on weighted Lebesgue spaces, On some sharp weighted norm inequalities, Representation of singular integrals by dyadic operators, and the \(A_2\) theorem, A rotation method which gives linear \(L^{p}\) estimates for powers of the Ahlfors--Beurling operator, Haar multipliers meet Bellman functions, Mixed \(A_p\)-\(A_r\) inequalities for classical singular integrals and Littlewood-Paley operators, The foundational inequalities of D. L. Burkholder and some of their ramifications, Burkholder's function via Monge-Ampère equation, Wavelet representation of singular integral operators, Limited range extrapolation with quantitative bounds and applications, The sharp weighted bound for general Calderón-Zygmund operators, Subordination by conformal martingales in \(L^{p}\) and zeros of Laguerre polynomials, New Bellman Functions and Subordination by Orthogonal Martingales in L p , 1 < p ≤ 2, Dyadic harmonic analysis beyond doubling measures, Weighted estimates for powers of the Ahlfors-Beurling operator, Sharp \(A_{2}\) inequality for Haar shift operators, Recovering singular integrals from Haar shifts, A boundedness criterion for singular integral operators of convolution type on the Fock space, Burkholder integrals, Morrey’s problem and quasiconformal mappings

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