Cones, rectifiability, and singular integral operators
Damian DąbrowskiUniversitat Autònoma de Barcelona, Spain
Let be a Radon measure on . We define and study conical energies , which quantify the portion of lying in the cone with vertex , direction , and aperture . We use these energies to characterize rectifiability and the big pieces of Lipschitz graphs property. Furthermore, if we assume that has polynomial growth, we give a sufficient condition for -boundedness of singular integral operators with smooth odd kernels of convolution type.
Cite this article
Damian Dąbrowski, Cones, rectifiability, and singular integral operators. Rev. Mat. Iberoam. 38 (2022), no. 4, pp. 1287–1334DOI 10.4171/RMI/1301