6533b871fe1ef96bd12d1b61

RESEARCH PRODUCT

Two examples related to conical energies

Damian Dąbrowski

subject

matematiikkasingular integral operatorsMetric Geometry (math.MG)Articlesbig pieces of Lipschitz graphsquantitative rectifiabilityconical densityMathematics - Metric GeometryMathematics - Classical Analysis and ODEs28A75 (Primary) 28A78 42B20 (Secondary)Classical Analysis and ODEs (math.CA)FOS: MathematicsCone

description

In a recent article 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 M\"{o}rters, the other is new and could be of independent interest as an example of a relatively ugly set containing big pieces of Lipschitz graphs.

yearjournalcountryeditionlanguage
2022-01-04
http://urn.fi/URN:NBN:fi:jyu-202201111059