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

By Oliver Dragičević, Alexander Volberg. 2003

59 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f3d48a13d5c627e0ab5431aa81aa1378f0046211

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Representation of singular integrals by dyadic operators, and the A_2 theorem (2011, background): “[14] Fedor Nazarov, Alexander Reznikov, and Alexander Volberg.”
The foundational inequalities of D.L. Burkholder and some of their ramifications (2010, unknown): “Nazarov, S. Treil and A. Volberg.”
The sharp weighted bound for general Calderón-Zygmund operators (2010, background): “th implications to Beltrami equations, the case of the Beurling–Ahlfors transform B ∈ L(L2(C)) was ﬁrst settled by Petermichl and Volberg [24], and with an alternative proof by Dragičević and Volberg [7]. Petermichl also obtained the sharp bounds for the Hilbert transform H ∈ L(L2(R)) [22], and then”
SHARP BOUNDS FOR GENERAL COMMUTATORS ON WEIGHTED LEBESGUE SPACES (2010, background): “So far the linear growth in L(2)(w) has been shown to hold for dyadic operators (martingale transform [29], dyadic square function [12], dyadic paraproduct [3]), or for operators who have lots of symmetries and can be written as averages of dyadic shift operators (such us the Hilbert transform [25],”
The sharp weighted bound for general Calderon-Zygmund operators (2010, unknown): “(45)] with implications to Beltrami equations, the case of the Beurling–Ahlfors transform B ∈L (L2(C)) was first settled by Petermichl and Volberg [29], and with an alternative proof by Dragičević and Volberg [7].”
Sharp A2 inequality for Haar shift operators (2009, background): “The operator T(σ·) is expanded in ‘Haar basis’, but as had been done prior papers, such as [7, 12, 16], the Haar bases are adapted to the two measures σ and μ.”