A rotation method which gives linear \(L^{p}\) estimates for powers of the Ahlfors--Beurling operator

DOI10.1016/j.matpur.2006.10.005zbMath1140.42303OpenAlexW2028959557MaRDI QIDQ864193

Stefanie Petermichl, Oliver Dragičević, Alexander Volberg

Publication date: 13 February 2007

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2006.10.005

zbMATH Keywords

Ahlfors--Beurling operatormethod of rotationsHaar systemsBurkholder's differential subordination Lemma

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Multipliers for harmonic analysis in several variables (42B15) Linear operators on function spaces (general) (47B38) Integral operators (47G10)

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Representation of singular integrals by dyadic operators, and the \(A_2\) theorem ⋮ The foundational inequalities of D. L. Burkholder and some of their ramifications ⋮ Sharp \(L^p\) estimates of powers of the complex Riesz transform ⋮ A method of rotations for Lévy multipliers ⋮ Asymptotic behavior of 𝐿^{𝑝} estimates for a class of multipliers with homogeneous unimodular symbols ⋮ An approach to rotating boundary layers based on vector Radon measures ⋮ Convexity of power functions and bilinear embedding for divergence-form operators with complex coefficients ⋮ Weighted estimates for powers of the Ahlfors-Beurling operator ⋮ Quantitative weighted estimates for rough homogeneous singular integrals ⋮ Some remarks on the \(L^p\) estimates for powers of the Ahlfors-Beurling operator ⋮ Weighted inequalities for multivariable dyadic paraproducts ⋮ Non-stretch mappings for a sharp estimate of the Beurling-Ahlfors operator ⋮ Stochastic three-dimensional rotating Navier-Stokes equations: averaging, convergence and regularity

Cites Work

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