Representation of singular integrals by dyadic operators, and the A(2) theorem

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Hytönen , T P 2017 , ' Representation of singular integrals by dyadic operators, and the A(2) theorem ' , Expositiones Mathematicae , vol. 35 , no. 2 , pp. 166-205 . https://doi.org/10.1016/j.exmath.2016.09.003

Title: Representation of singular integrals by dyadic operators, and the A(2) theorem
Author: Hytönen, Tuomas P.
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2017
Language: eng
Number of pages: 40
Belongs to series: Expositiones Mathematicae
ISSN: 0723-0869
URI: http://hdl.handle.net/10138/307045
Abstract: This exposition presents a self-contained proof of the A(2) theorem, the quantitatively sharp norm inequality for singular integral operators in the weighted space L-2 (w). The strategy of the proof is a streamlined version of the author's original one, based on a probabilistic Dyadic Representation Theorem for singular integral operators. While more recent non-probabilistic approaches are also available now, the probabilistic method provides additional structural information, which has independent interest and other applications. The presentation emphasizes connections to the David-Journe T(1) theorem, whose proof is obtained as a byproduct. Only very basic Probability is used; in particular, the conditional probabilities of the original proof are completely avoided. (C) 2016 Elsevier GmbH. All rights reserved.
Subject: Singular integral
Calderon-Zygmund operator
Weighted norm inequality
Sharp estimate
A(2) theorem
T(1) theorem
CALDERON-ZYGMUND OPERATORS
AHLFORS-BEURLING OPERATOR
WEIGHTED LEBESGUE SPACES
POINTWISE ESTIMATE
HILBERT TRANSFORM
MAXIMAL-FUNCTION
AP WEIGHTS
BOUNDS
EXTRAPOLATION
INEQUALITIES
111 Mathematics
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