A Simple Proof of the A2 Conjecture

By Andrei K. Lerner. 2013

291 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d77dd455b724358d62d1c172d9838985d21a21b5

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

A Fractional Muckenhoupt–Wheeden Theorem and its Consequences (2013, background): “(For the history of these results, see [12,13,17] and the references they contain.”
The Sharp Weighted Bound for Multilinear Maximal Functions and Calderón–Zygmund Operators (2012, background): “2) Again, we refer the reader to [5,10,15,17] for the background material and further references.”
Multiple Vector Valued Inequalities via the Helicoidal Method (2015, background): “The collections of intervals constitute a maximal covering for the level sets of certain maximal operators, and for that reason, they form a sparse collection of intervals (in the sense of [Ler13]).”
Sharp weighted bounds for the q‐variation of singular integrals (2012, methodology): “For these special shifts, the ideas of Lerner [12, 13] simplify the proof of Proposition 4.”
Quantitative weighted estimates for rough homogeneous singular integrals (2015, background): “Lerner [16, 17], and keeps developing with new extensions, among them the recent approach of M.”
Sharp weighted bounds without testing or extrapolation (2012, background): “called Haar shift operators [5]. Another way is to use families of sparse cubes. Let S ⊂ D be a sparse family and deﬁne sparse Caldero´n-Zygmund operator TSf := X Q∈S − Z Q f dx·χQ. 4 KABEMOEN Lerner [15, 16] proved the corresponding version of Theorem 2.1 for Caldero´n-Zygmund operators. Theorem 2.”
On Sharp Aperture-Weighted Estimates for Square Functions (2013, methodology): “In particular, similarly to [14], we obtain the X((2))-norm boundedness of B by A on an arbitrary Banach function space X .”
A sparse domination principle for rough singular integrals (2016, unknown): “n weak endpoint estimates for maximal truncations. 1. Introductionandmainresults Singular integral operators of Calderón-Zygmund type, which are a priori signed and nonlocal, can be dominated in norm [23], pointwise [8, 19, 22], or dually [2, 10, 11] by sparse averaging operators (forms), which are ”
Boundedness of commutators of fractional integral operators on mixed Morrey spaces (2019, methodology): “We make use of the dyadic local sharp maximal function defined in [43] together with a key formula [43, Theorem 2.”
Sparse Domination Theorem for Multilinear Singular Integral Operators with $L^{r}$-Hörmander Condition (2016, unknown): “1, 2, 3, 5 [21] A. Lerner and F. Nazarov, Intuitive dyadic calculus: the basics.”
One and two weight norm inequalities for Riesz potentials (2012, background): “ integrals, which has been studied intensively for more than a decade, and was recently solved in full generality by Hyto¨nen [12]. For the complete history of the problem we also refer the reader to [2, 18, 22, 24, 32] and the references they contain. The problem of sharp constants for Riesz potent”
Sparse bilinear forms for Bochner Riesz multipliers and applications (2016, unknown): “After that, Lerner-Nazarov [26] and Conde-Rey [11] simultaneously simpliﬁed the norm control by a pointwise bound.”
Sharp weighted norm estimates beyond Calderón–Zygmund theory (2015, unknown): “…this extra property, we are going to detail an “elementary” proof of the sharp weighted estimates (simpler than all the existing proofs, such as [Lerner 2013b; Lacey 2015]), which has also the very important property that is extends to nonintegral operators with no regularity property on the…”
Representation of singular integrals by dyadic operators, and the A_2 theorem (2011, methodology): “[13] Andrei K. Lerner.”