Bart, V. A. 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. Reviewer: V.Grebenev (Novosibirsk) Cited in 1 Document 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 Keywords:holomorphic function; Carleman-Krylov-Goluzin formula; Patil theorem; \(H^1\)-space; convergence Citations:Zbl 0892.93004 PDFBibTeX XMLCite \textit{V. A. Bart}, Probl. Mat. Anal. 21, 45--67 (2000; Zbl 0987.32001); translation from Probl. Mat. Anal. 21, 45--67 (2000)