Estimates for the norms of the Carleman-Goluzin-Krylov operators in the disk algebra and the Hardy space \(H^1\) (Q2773587)
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scientific article; zbMATH DE number 1710221
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Estimates for the norms of the Carleman-Goluzin-Krylov operators in the disk algebra and the Hardy space \(H^1\) |
scientific article; zbMATH DE number 1710221 |
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24 February 2002
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holomorphic function
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Carleman-Krylov-Goluzin formula
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Patil theorem
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\(H^1\)-space
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convergence
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Estimates for the norms of the Carleman-Goluzin-Krylov operators in the disk algebra and the Hardy space \(H^1\) (English)
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The author studies the following problem posed by \textit{J. R.~Partington} in [Interpolation, identification, and sampling, Clarendon Press, Oxford (1997; Zbl 0892.93004)]: Is it possible to apply the Patil theorem to prove convergence in the disk algebra and in the Hardy space \(H^1\)?NEWLINENEWLINENEWLINEIn general, the author gives a negative answer to the question and shows that there exists a class of functions for which the Carleman-Krylov-Goluzin formula does not hold.
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