Carleson measures, trees, extrapolation, and T(b) theorems

By P. Auscher, S. Hofmann, Camil Muscalu, Terence Tao, C. Thiele. 2001

106 citations recorded by the source corpus.

The theory of Carleson measures, stopping time arguments, and atomic decompositions has been well-established in harmonic analysis. More recent is the theory of phase space analysis from the point of view of wave packets on tiles, tree selection algorithms, and tree size estimates. The purpose of this paper is to demonstrate that the two theories are in fact closely related, by taking existing results and reproving them in a unified setting. In particular we give a dyadic version of extrapolation for Carleson measures, as well as a two-sided local dyadic T(b) theorem which generalizes earlier T(b) theorems of David, Journe, Semmes, and Christ.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aeddf5e2d60ffb7255cdd539d9003cfcfa8a1ca9

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Uniform Rectifiability, Carleson measure estimates, and approximation of harmonic functions (2014, methodology): “ly requires only that E have a dyadic cube structure, and that σ be a non-negative, dyadically doubling Borel measure onE. Proof of Lemma 4.5. The proof proceeds by induction, following [LM], [AHLT], [AHMTT], [HM2]. The induction hypothesis, which we formulate for any a ≥ 0, is as follows: H(a) Ther”
Analyticity of layer potentials and $L^{2}$ solvability of boundary value problems for divergence form elliptic equations with complex $L^{\infty}$ coefficients (2007, unknown): “dyadic” Calder´ on-Zygmund kernels, appears in [ AHMTT ].”
Sharp A2 inequality for Haar shift operators (2009, background): “A subtle corona decomposition is central to [15], and the paper [1] includes several examples in the context of dyadic analysis.”
$L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets (2013, background): “Further extensions of the local T (b) theory for singular integrals appear in [5], [7], [6] and [51].”