Bilipschitz maps, analytic capacity, and the Cauchy integral

By X. Domènech. 2005

79 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9731fbbb5a9212835ab65558edac37b5315e05bc

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

SHARP MAXIMAL INEQUALITIES AND COMMUTATORS ON MORREY SPACES WITH NON-DOUBLING MEASURES (2007, unknown): “Tolsa showed that the analytic capacity is subadditive and that it is bi-Lipschitz invariant [17, 18].”
GENERALIZED FRACTIONAL INTEGRALS AND THEIR COMMUTATORS OVER NON-HOMOGENEOUS METRIC MEASURE SPACES (2013, background): “1) has proved to play a striking role in solving the long-standing open Painlevé’s problem and Vitushkin’s conjecture by Tolsa [40, 41, 42].”
Two Weight Inequalities for Discrete Positive Operators (2009, background): “Consult the corona decomposition in [22], and the paper [1] includes several examples in the context of dyadic analysis.”
An analyst’s traveling salesman theorem for sets of dimension larger than one (2016, background): “The result has applications to harmonic measure [8], Kleinian groups [9], analytic capacity [34], and brownian motion [10].”
Extra cancellation of even Calderón–Zygmund operators and quasiconformal mappings (2008, background): “nderstanding of the nature of removable sets for bounded quasi-regular functions (see [ACMOU], [CFMOZ] and [CT]). Since bilipschitz mappings preserve removable sets for bounded holomorphic functions ([T]), the Theorem immediately says that the removable sets for bounded µ-quasi-regular functions, wi”
BOUNDEDNESS OF MULTILINEAR COMMUTATORS OF CALDERÓN-ZYGMUND OPERATORS ON ORLICZ SPACES OVER NON-HOMOGENEOUS SPACES (2012, background): “However, in recent years, many results in the classical theory of Calderón-Zygmund operators on R have been proved still valid with the Lebesgue measure m replaced by a Radon measure μ satisfying the polynomial growth condition (see, for example, [22, 23, 24, 25, 26, 27, 17, 3, 7, 8]).”
Uniform rectifiability, Calderón–Zygmund operators with odd kernel, and quasiorthogonality (2008, unknown): “See also [12, 19, 20] for some related techniques.”
The Tb-theorem on non-homogeneous spaces that proves a conjecture of Vitushkin (2014, methodology): “ have already made a remark that the second claim follows from the ﬁrst one combined with Theorem 1. Before proving Theorem 1, we would like to present its beautiful application found by Xavier Tolsa [XT2]. Recall that R(x,y,z) denotes the radius of the circle passing through x,y,z∈ C. We will call ”