×

Estimates for the norms of the Carleman-Goluzin-Krylov operators in the disk algebra and the Hardy space \(H^1\). (English. Russian original) Zbl 0987.32001

J. Math. Sci., New York 105, No. 5, 2330-2346 (2001); translation from Probl. Mat. Anal. 21, 45-67 (2000).
The author studies the following problem posed by 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 \(H^1\)?
In 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.

MSC:

32A35 \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables
32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables

Citations:

Zbl 0892.93004
PDFBibTeX XMLCite