# 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
Two examples related to conical energies
In a recent article [Dąb20] we introduced and studied conical energies. We used them to prove three results: a characterization of rectifiable measures, a characterization of sets with big pieces ofExpand
Radon measures and Lipschitz graphs
• Mathematics
• 2020
For all $1\leq m\leq n-1$, we investigate the interaction of locally finite measures in $\mathbb{R}^n$ with the family of $m$-dimensional Lipschitz graphs. For instance, we characterize RadonExpand

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