TY - JOUR
T1 - Uniform rectifiability, Calderón-Zygmund operators with odd kernel, and quasiorthogonality
AU - Tolsa, Xavier
PY - 2009/3/1
Y1 - 2009/3/1
N2 - 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 script C sign2 are bounded in L 2(μ), if μ is an n-dimensional uniformly rectifiable measure. © 2008 London Mathematical Society.
AB - 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 script C sign2 are bounded in L 2(μ), if μ is an n-dimensional uniformly rectifiable measure. © 2008 London Mathematical Society.
U2 - https://doi.org/10.1112/plms/pdn035
DO - https://doi.org/10.1112/plms/pdn035
M3 - Article
VL - 98
SP - 393
EP - 426
JO - Proceedings of the London Mathematical Society
JF - Proceedings of the London Mathematical Society
SN - 0024-6115
ER -