Abstract
We develop a potential theory for a Riesz type kernel in a homogeneous space and characterize the compact sets K with capacity zero as the sets K for which every continous function f on K is the restriction to K of a continuous potential \(U^{\sigma _{f}}_{k}\) of an absolutely continuous measure σ f supported in an arbitrarily small neighbourhood of K. The measure σ f can be choosen as a suitable restriction of a single measure σ that only depends on the set K and the kernel k.
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Sjödin, T. Continuous Functions and Riesz Type Potentials in Homogeneous Spaces. Potential Anal 43, 495–511 (2015). https://doi.org/10.1007/s11118-015-9483-4
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DOI: https://doi.org/10.1007/s11118-015-9483-4
Keywords
- Homogeneous space
- Doubling measure
- Kernel
- Potential
- Energy
- Capacity
- Capacitary potential
- Approximate identity
- Dyadic cubes