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 Mat. Sb. (N.S.), 1985, Volume 128(170), Number 3(11), Pages 364–382 (Mi msb2165)

On the Cauchy–Riemann conditions in the class of functions with summable modulus, and some boundary properties of analytic functions

G. Kh. Sindalovskii

Abstract: The analyticity of functions that satisfy the Cauchy-Riemann conditions and have summable modulus is established. Thus the Looman–Men'shov and Tolstov theorems are generalized. The theorem of Lindelöf is generalized (from the class of bounded functions to the class $L_1$) for certain kinds of domains. Sufficient criteria for continuity on the boundary for some classes of analytic functions are investigated.
Bibliography: 21 titles.

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English version:
Mathematics of the USSR-Sbornik, 1987, 56:2, 359–377

Bibliographic databases:

UDC: 517.53
MSC: 30A05, 30C80

Citation: G. Kh. Sindalovskii, “On the Cauchy–Riemann conditions in the class of functions with summable modulus, and some boundary properties of analytic functions”, Mat. Sb. (N.S.), 128(170):3(11) (1985), 364–382; Math. USSR-Sb., 56:2 (1987), 359–377

Citation in format AMSBIB
\Bibitem{Sin85} \by G.~Kh.~Sindalovskii \paper On the Cauchy--Riemann conditions in the class of functions with summable modulus, and some boundary properties of analytic functions \jour Mat. Sb. (N.S.) \yr 1985 \vol 128(170) \issue 3(11) \pages 364--382 \mathnet{http://mi.mathnet.ru/msb2165} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=815270} \zmath{https://zbmath.org/?q=an:0607.30004|0593.30002} \transl \jour Math. USSR-Sb. \yr 1987 \vol 56 \issue 2 \pages 359--377 \crossref{https://doi.org/10.1070/SM1987v056n02ABEH003041} 

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This publication is cited in the following articles:
1. D. S. Telyakovskii, “Generalization of a theorem of Men'shov on monogenic functions”, Math. USSR-Izv., 35:1 (1990), 221–231
2. Rao N., “A Generalization of the Looman-Menchoff Theorem”, Isr. J. Math., 70:1 (1990), 93–103
3. E. P. Dolzhenko, “The work of D. E. Men'shov in the theory of analytic functions and the present state of the theory of monogeneity”, Russian Math. Surveys, 47:5 (1992), 71–102
4. Dolzhenko E., “Menshoff,D.Y. and the Modern State of Monogenic Theory”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1992, no. 4, 24–36
5. Rao N., “A Note on Tolstov's Theorem on Harmonic Functions in the Plane”, Math. Scand., 78:2 (1996), 178–182
6. Ryabykh V.G., “Ekstremalnye funktsii lineinogo funktsionala nad prostranstvom bergmana \it{n}'_{1}”, Izvestiya vysshikh uchebnykh zavedenii. Severo-Kavkazskii region. Seriya: Estestvennye nauki, 2012, no. 2, 26–30
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