Two examples related to conical energies

Authors

  • Damian Dąbrowski Universitat Autònoma de Barcelona, Departament de Matemàtiques and Barcelona Graduate School of Mathematics (BGSMath); and University of Jyväskylä, Department of Mathematics and Statistics
DOI: https://doi.org/10.54330/afm.113378

Keywords:

Cone, conical density, quantitative rectifiability, big pieces of Lipschitz graphs, singular integral operators

Abstract

In a recent article (2021) 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 of Lipschitz graphs, and a sufficient condition for boundedness of nice singular integral operators. In this note we give two examples related to sharpness of these results. One of them is due to Joyce and Mörters (2000), the other is new and could be of independent interest as an example of a relatively ugly set containing big pieces of Lipschitz graphs.
Issue
Vol. 47 No. 1 (2022)
Section
Articles

Published

2022-01-04

How to Cite

Dąbrowski, D. (2022). Two examples related to conical energies. Annales Fennici Mathematici, 47(1), 261–281. https://doi.org/10.54330/afm.113378

Copyright (c) 2021 Annales Fennici Mathematici

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.