Cones, rectifiability, and singular integral operators

@article{Dkabrowski2021ConesRA,
  title={Cones, rectifiability, and singular integral operators},
  author={Damian Dkabrowski},
  journal={Revista Matem{\'a}tica Iberoamericana},
  year={2021}
}
Let μ be a Radon measure on R. We define and study conical energies Eμ,p(x, V, α), which quantify the portion of μ lying in the cone with vertex x ∈ R , direction V ∈ G(d, d−n), and aperture α ∈ (0, 1). We use these energies to characterize rectifiability and the big pieces of Lipschitz graphs property. Furthermore, if we assume that μ has polynomial growth, we give a sufficient condition for L(μ)-boundedness of singular integral operators with smooth odd kernels of convolution type. 
2 Citations
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