Abstract
We prove that a compact subset of the complex plane satisfies a local Markov inequality if and only if it satisfies a Kolmogorov type inequality. This result generalizes a theorem established by Bos and Milman in the real case. We also show that every set satisfying the local Markov inequality is a sum of Cantor type sets which are regular in the sense of the potential theory.
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Białas-Cież, L., Eggink, R. Equivalence of the Local Markov Inequality and a Kolmogorov Type Inequality in the Complex Plane. Potential Anal 38, 299–317 (2013). https://doi.org/10.1007/s11118-012-9274-0
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DOI: https://doi.org/10.1007/s11118-012-9274-0
Keywords
- Markov inequality
- Kolmogorov inequality
- Green function
- L-regularity of sets
- Holomorphic functions
- Cantor sets