Calderón-Zygmund kernels and rectifiability in the plane

DOI10.1016/j.aim.2012.04.025zbMath1258.42013arXiv1110.1302OpenAlexW2095371973MaRDI QIDQ436183

J. Herrera, H. S. Yoon

Publication date: 30 July 2012

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.1302

zbMATH Keywords

singular integralCauchy transformrectifiability

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25)

Related Items

The Huovinen transform and rectifiability of measures, Nonnegative kernels and 1-rectifiability in the Heisenberg group, Some Calderón-Zygmund kernels and their relations to Wolff capacities and rectifiability, Capacities associated with Calderón-Zygmund kernels, Symmetrization of a Cauchy-like kernel on curves, A new family of singular integral operators whose \(L^2\)-boundedness implies rectifiability, Singular Integrals on Self-similar Subsets of Metric Groups, Square functions and uniform rectifiability, L^2-bounded singular integrals on a purely unrectifiable set in R^d, A family of singular integral operators which control the Cauchy transform, Singular integrals unsuitable for the curvature method whose \(L^2\)-boundedness still implies rectifiability

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rectifiable sets and the traveling salesman problem
• L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
• Unrectifiable 1-sets have vanishing analytic capacity
• Menger curvature and rectifiability
• Painlevé's problem and the semiadditivity of analytic capacity.
• The Cauchy integral, analytic capacity, and uniform rectifiability
• A nicely behaved singular integral on a purely unrectifiable set
• Opérateurs intégraux singuliers sur certaines courbes du plan complexe
• Opérateurs d'intégrale singulière sur les surfaces régulières
• The boundedness of Riesz 𝑠-transforms of measures in ℝⁿ
• Cauchy integrals on Lipschitz curves and related operators
• Analytic capacity: discrete approach and curvature of measure