RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

This article is cited in 6 scientific papers (total in 6 papers)

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.

Full text: PDF file (1221 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.53
MSC: 30A05, 30C80
Received: 23.07.1984

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}


Linking options:
  • http://mi.mathnet.ru/eng/msb2165
  • http://mi.mathnet.ru/eng/msb/v170/i3/p364

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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  mathnet  crossref  mathscinet  zmath
    2. Rao N., “A Generalization of the Looman-Menchoff Theorem”, Isr. J. Math., 70:1 (1990), 93–103  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    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  mathscinet  isi
    5. Rao N., “A Note on Tolstov's Theorem on Harmonic Functions in the Plane”, Math. Scand., 78:2 (1996), 178–182  mathscinet  zmath  isi
    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  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:372
    Full text:114
    References:34

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020