102
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Euclidean maximum moduli of plane domains and their applications

Pages 1869-1880 | Received 09 Sep 2018, Accepted 18 Dec 2018, Published online: 02 Jan 2019

References

  • Ahlfors LV. Conformal invariants, topics in geometric function theory. New York: McGraw-Hill; 1973.
  • Avkhadiev FG, Wirths KJ. Schwarz–Pick type inequalities. Basel–Boston–Berlin: Birkhäuser Verlag; 2009.
  • Pommerenke Ch. Uniformly perfect sets and the Poincaré metric. Arch Math. 1979;32:192–199. doi: 10.1007/BF01238490
  • Beardon AF, Pommerenke Ch. The Poincaré metric of plane domains. J London Math Soc (2). 1978;s2-18:475–483. doi: 10.1112/jlms/s2-18.3.475
  • Avkhadiev FG, Aksent'ev LA. The main results on sufficient condition for an analytic function to be schlicht. Russ Math Surv. 1975;30(4):1–63. doi: 10.1070/RM1975v030n04ABEH001511
  • Harmelin R. Locally convex functions and the Schwarzian derivative. Israel J Math. 1989;67:367–379. doi: 10.1007/BF02764954
  • Ma W, Minda D. Behavior of domain constants under conformal mappings. Israel J Math. 1995;91:157–171. doi: 10.1007/BF02761644
  • Pommerenke Ch. Linear-invariante Familien analitischer Functionen. I. Math Ann. 1964;155:108–154. doi: 10.1007/BF01344077
  • Balinsky AA, Evans WD, Lewis RT. The analysis and geometry of Hardy's inequality. Heidelberg–New York–Dordrecht–London: Springer; 2015. (Universitext).
  • Avkhadiev FG. Hardy type inequalities in higher dimensions with explicit estimate of constants. Lobachevskii J Math. 2006;21:3–31.
  • Avkhadiev FG. Integral inequalities in hyperbolic-type domains and their application. Sbornik. 2015;206(12):1657–1681. doi: 10.1070/SM2015v206n12ABEH004508
  • Avkhadiev FG. Hardy-Rellich inequalities in domains of the Euclidean space. J Math Anal Appl. 2016;442:469–484. doi: 10.1016/j.jmaa.2016.05.004
  • Avkhadiev FG. Sharp Hardy constants for annuli. J Math Anal Appl. 2018;466:936–951. doi: 10.1016/j.jmaa.2018.06.031

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.