Illinois Journal of Mathematics

Null sets for the capacity associated to Riesz kernels

Laura Prat

Full-text: Open access

Abstract

We prove that the capacity associated to the signed vector-valued Riesz kernel $\frac{x}{|x|^{1+\alpha}}$ in $\Rn$, $0<\alpha<n$, $\alpha\notin\Z$, vanishes on compact sets with finite $\alpha$-Hausdorff measure that satisfy an additional density condition.

Article information

Source
Illinois J. Math., Volume 48, Number 3 (2004), 953-963.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258131063

Digital Object Identifier
doi:10.1215/ijm/1258131063

Mathematical Reviews number (MathSciNet)
MR2114262

Zentralblatt MATH identifier
1070.42009

Subjects
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 28A12: Contents, measures, outer measures, capacities

Citation

Prat, Laura. Null sets for the capacity associated to Riesz kernels. Illinois J. Math. 48 (2004), no. 3, 953--963. doi:10.1215/ijm/1258131063. https://projecteuclid.org/euclid.ijm/1258131063


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