Skip to Main Content

St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Branching points area theorems for univalent functions
HTML articles powered by AMS MathViewer

by S. Shimorin
St. Petersburg Math. J. 18 (2007), 141-181
DOI: https://doi.org/10.1090/S1061-0022-07-00947-8
Published electronically: January 24, 2007

Abstract:

Area theorems of a new type are obtained by considering branching point compositions with univalent functions. Such theorems can be formulated both in the form of integral estimates and in the form of Grunsky and Goluzin-type inequalities.
References
  • N. Abuzyarova and H. Hedenmalm, Branch point area methods in conformal mapping, J. Anal. Math. (to appear).
  • S. Bergman and M. Schiffer, Kernel functions and conformal mapping, Compositio Math. 8 (1951), 205–249. MR 39812
  • János Bognár, Indefinite inner product spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 78, Springer-Verlag, New York-Heidelberg, 1974. MR 0467261
  • Lennart Carleson, A representation formula for the Dirichlet integral, Math. Z. 73 (1960), 190–196. MR 112958, DOI 10.1007/BF01162477
  • Peter L. Duren, Univalent functions, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 259, Springer-Verlag, New York, 1983. MR 708494
  • G. M. Goluzin, Geometricheskaya teoriya funktsiĭ kompleksnogo peremennogo, 2nd ed., Izdat. “Nauka”, Moscow, 1966 (Russian). Edited by V. I. Smirnov; With a supplement by N. A. Lebedev, G. V. Kuzmina and Ju. E. Alenicyn. MR 0219714
  • Håkan Hedenmalm and Serguei Shimorin, Weighted Bergman spaces and the integral means spectrum of conformal mappings, Duke Math. J. 127 (2005), no. 2, 341–393. MR 2130416, DOI 10.1215/S0012-7094-04-12725-3
  • N. A. Lebedev, Printsip ploshchadeĭ v teorii odnolistnykh funktsiĭ, Izdat. “Nauka”, Moscow, 1975 (Russian). MR 0450540
  • Zeev Nehari, Inequalities for the coefficients of univalent functions, Arch. Rational Mech. Anal. 34 (1969), 301–330. MR 247061, DOI 10.1007/BF00248571
  • Christian Pommerenke, Univalent functions, Studia Mathematica/Mathematische Lehrbücher, Band XXV, Vandenhoeck & Ruprecht, Göttingen, 1975. With a chapter on quadratic differentials by Gerd Jensen. MR 0507768
  • H. Prawitz, Über Mittelwerte analytischer Funktionen, Arkiv Mat. Astronomy Fysik 20A (1927–1928), no. 6, 1–12.
  • Serguei Shimorin, A multiplier estimate of the Schwarzian derivative of univalent functions, Int. Math. Res. Not. 30 (2003), 1623–1633. MR 1979583, DOI 10.1155/S107379280321223X
Similar Articles
  • Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 30C50
  • Retrieve articles in all journals with MSC (2000): 30C50
Bibliographic Information
  • S. Shimorin
  • Affiliation: Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden
  • Email: shimorin@math.kth.se
  • Received by editor(s): October 10, 2005
  • Published electronically: January 24, 2007
  • © Copyright 2007 American Mathematical Society
  • Journal: St. Petersburg Math. J. 18 (2007), 141-181
  • MSC (2000): Primary 30C50
  • DOI: https://doi.org/10.1090/S1061-0022-07-00947-8
  • MathSciNet review: 2225218