Uniform rectifiability, Calderón–Zygmund operators with odd kernel, and quasiorthogonality
By Xavier Tolsa. 2008
86 citations recorded by the source corpus.
In this paper we study some questions in connection with uniform rectifiability and the L2 boundedness of Calderón–Zygmund operators (CZOs). We show that uniform rectifiability can be characterized in terms of some new adimensional coefficients that are related to the Jones’ β numbers. We also use these new coefficients to prove that n‐dimensional CZOs with odd kernel of type 𝒞2 are bounded in L2(μ), if μ is an n‐dimensional uniformly rectifiable measure.
Subfields: Applied Mathematics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/5504fde0d8bf927d26d613d6576ac0baf52130d8
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In Applied Mathematics
- Gilad Lerman
- J. Tyler Whitehouse
- Xavier Tolsa
- Tuomas Hytönen
- Dachun Yang
- Wen Yuan
- Xing Fu
- Yoshihiro Sawano
In Numerical Analysis
Citations in the corpus
- Characterization of n-rectifiability in terms of Jones’ square function: part I (2015, methodology): “Other coefficients which involve a variant of the Wasserstein distance W1 in the spirit of the βμ,p’s have been introduced in [18] and have shown to be useful in the study of different questions regarding the connection between uniform n-rectifiability and the boundedness of”
- High-Dimensional Menger-Type Curvatures - Part I: Geometric Multipoles and Multiscale Inequalities (2008, background): “The main development of the paper (implying this Carleson-type estimate) is a careful bound on the Menger-type curvature of an Ahlfors regular measure in terms of the sizes of least squares approximations of that measure at different scales and locations.”