Principal values for Riesz transforms and rectifiability
By Xavier Tolsa. 2007
54 citations recorded by the source corpus.
Let $E\subset R^d$ with $H^n(E) \ve} \frac{x-y}{|x-y|^{n+1}} dH^n(y)$$ exists H^n-almost everywhere in E. To prove this result we obtain precise estimates from above and from below for the $L^2$ norm of the n-dimensional Riesz transforms on Lipschitz graphs.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6e229ec8a39192ad99ea1ec440a7a6a3d6d2488e
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- M. Mitrea
- S. Hofmann
- Michael Taylor
- Xavier Tolsa
- Dachun Yang
- P. Auscher
- Tuomas Hytönen
- J. M. Martell
In Mathematical Physics
- M. Mitrea
- S. Hofmann
- Xavier Tolsa
- Michael Taylor
- Dachun Yang
- Tuomas Hytönen
- P. Auscher
- Xuan Thinh Duong
Citations in the corpus
- Uniform rectifiability, Calderón–Zygmund operators with odd kernel, and quasiorthogonality (2008, methodology): “be a useful tool to study the aforementioned problem of proving that the L(2)(μ) boundedness of the Riesz transform Rμ implies the uniform rectifiability of μ when μ is AD regular, as well as other related problems (see [21] for a recent application concerning the existence of principal values for R”
- Characterization of n-rectifiability in terms of Jones’ square function: part I (2015, background): “n-dimensional singular integral operators (see [14,19], for example).”
- Singular Integrals and Elliptic Boundary Problems on Regular Semmes–Kenig–Toro Domains (2009, background): “Regarding the nature of the principal value integrals associated with the Riesz kernels, a recent result from [115] states that if E ⊂ Rn+1 has Hn(E) < ∞, then E is countably rectifiable (of dimension n) ⇐⇒ (3.”