Equivalence of the Local Markov Inequality and a Kolmogorov Type Inequality in the Complex Plane |
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Authors: | Leokadia Białas-Cież Raimondo Eggink |
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Affiliation: | 1. Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. ?ojasiewicza 6, 30-348, Kraków, Poland
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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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