Estimation of intermediate derivatives and a Bang-type theorem. I (Q2786967)
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scientific article; zbMATH DE number 6545125
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Estimation of intermediate derivatives and a Bang-type theorem. I |
scientific article; zbMATH DE number 6545125 |
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Estimation of intermediate derivatives and a Bang-type theorem. I (English)
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24 February 2016
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estimates for intermediate derivatives
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quasismooth arc
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quasianalytic classes of functions
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0.8623391
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0.8559016
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0.8557873
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0.85413957
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The author extends the classical Cartan-Gorny-Kolmogorov bounds for intermediate derivatives of smooth functions on the real line to the case of functions on quasismooth arcs in the complex plane (a Jordan arc \(\gamma\) is said to be quasismooth if for every pair \(z,\xi\) of points of \(\gamma\), the length of the part of \(\gamma\) between \(z\) and \(\xi\) is bounded by \( c| z-\xi|\) where \(c\) is a constant). Regularization and quasianalyticity results for Carleman classes on suitable quasismooth arcs are then obtained in the spirit of Bang's proof of the Denjoy-Carleman theorem.
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