Extrapolation of Carleson measures and the analyticity of Kato's square-root operators

By P. Auscher, S. Hofmann, John L. Lewis, P. Tchamitchian. 2001

92 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c78971f2e2a88b6af01489f10f226806ac49eb07

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In Applied Mathematics

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Citations in the corpus

Hardy and BMO spaces associated to divergence form elliptic operators (2006, background): “is fact later in conjunction with the fact that every f ∈ BMOp L(R n) satisﬁes (9.9). 10 John-Nirenberginequality We start with the following auxiliary result, which is a modiﬁcation of Lemma 2.14 in [7]. Lemma 10.1 Suppose there exist numbers 0 < α < 1 and 0 < N < ∞ such that for some f”
$L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets (2013, background): “1 with a weak type JohnNirenberg lemma for Carleson measures, the Euclidean version of which appears in [4].”
Uniform Rectifiability, Carleson measure estimates, and approximation of harmonic functions (2014, methodology): “f actually 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”
Analyticity of layer potentials and $L^{2}$ solvability of boundary value problems for divergence form elliptic equations with complex $L^{\infty}$ coefficients (2007, background): “(n = 2), [ AHLT ] (when B is a perturbation of a real, symmetric matrix), [HLMc] (when the kernel of the heat semi-group e−tJ has a Gaussian upper bound) and [AHLMcT] in general6.”
Quadratic estimates and functional calculi of perturbed Dirac operators (2004, unknown): “This result was proved in a series of papers by Hofmann– McIntosh [18], Auscher–Hofmann–Lewis–Tchamitchian [3], Hofmann– Lacey–McIntosh [17], and, in full generality, by Auscher–Hofmann–Lacey–”
Carleson measures, trees, extrapolation, and T(b) theorems (2001, methodology): “theory and BMO [28], boundedness of singular integrals, square functions and maximal functions (e.g. [12], [22], [35], [50], [37], [38]), geometric measure theory (e.g. [24], [35, 36]), and PDE (e.g. [3], [27], [32], [42]). Moreover, via their connection with the theory of trees, Carleson measures h”