Table of Contents Author Guidelines Submit a Manuscript
Table of Contents Alerts

To receive news and publication updates for Abstract and Applied Analysis, enter your email address in the box below.

Abstract and Applied Analysis
Volume 2011, Article ID 259796, 11 pages
http://dx.doi.org/10.1155/2011/259796
Research Article

Univalent Functions in the Möbius Invariant 𝑄 𝐾 Space

Fernando Pérez-González1 and Jouni Rättyä2

1Departamento de Análisis Matemático, Universidad de La Laguna, Tenerife 38271 La Laguna, Spain
2Department of Physics and Mathematics, University of Eastern Finland, Campus of Joensuu, P.O. Box 111, 80101 Joensuu, Finland

Received 7 July 2011; Accepted 31 August 2011

Academic Editor: Svatoslav Staněk

Copyright © 2011 Fernando Pérez-González and Jouni Rättyä. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. L. Duren, Univalent Functions, vol. 259, Springer, New York, NY, USA, 1983.
  2. C. Pommerenke, Univalent Functions, Vandenhoeck & Ruprecht, Göttingen, Germany, 1975.
  3. C. Pommerenke, Boundary Behaviour of Conformal Maps, vol. 299, Springer, Berlin, Germany, 1992.
  4. P. L. Duren, Theory of Hp Spaces, Academic Press, New York, NY, USA, 1970.
  5. J. B. Garnett, Bounded Analytic Functions, vol. 96 of Pure and Applied Mathematics, Academic Press, New York, NY, USA, 1981.
  6. G. H. Hardy and J. E. Littlewood, β€œSome properties of fractional integrals. II,” Mathematische Zeitschrift, vol. 34, no. 1, pp. 403–439, 1932. View at Publisher Β· View at Google Scholar
  7. C. Pommerenke, β€œÜber die Mittelwerte und Koeffizienten multivalenter Funktionen,” Mathematische Annalen, vol. 145, pp. 285–296, 1961/1962. View at Google Scholar
  8. H. Prawitz, β€œUber Mittelwerte analytischer Funktionen,” Arkiv för Matematik, Astronomi och Fysik, vol. 20, pp. 1–12, 1927. View at Google Scholar
  9. A. Baernstein II, D. Girela, and J. A. Peláez, β€œUnivalent functions, Hardy spaces and spaces of Dirichlet type,” Illinois Journal of Mathematics, vol. 48, no. 3, pp. 837–859, 2004. View at Google Scholar
  10. D. Girela, M. Pavlović, and J. A. Peláez, β€œSpaces of analytic functions of Hardy-Bloch type,” Journal d'Analyse Mathématique, vol. 100, pp. 53–81, 2006. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  11. F. Pérez-González and J. Rättyä, β€œUnivalent functions in Hardy, Bergman, Bloch and related spaces,” Journal d'Analyse Mathématique, vol. 105, pp. 125–148, 2008. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  12. P. Galanopoulos, D. Girela, and R. Hernández, β€œUnivalent functions, VMOA and related spaces,” Journal of Geometric Analysis, vol. 21, no. 3, pp. 665–682, 2011. View at Google Scholar
  13. C. González and J. A. Peláez, β€œUnivalent functions in Hardy spaces in terms of the growth of arc-length,” Journal of Geometric Analysis, vol. 19, no. 4, pp. 755–771, 2009. View at Google Scholar
  14. A. Baernstein II, β€œAnalytic functions of bounded mean oscillation,” in Aspects of Contemporary Complex Analysis, D. Brannan and J. Clunie, Eds., pp. 3–36, Academic Press, London, UK, 1980. View at Google Scholar Β· View at Zentralblatt MATH
  15. C. Pommerenke, β€œSchlichte Funktionen und analytische Funktionen von beschränkter mittlerer Oszillation,” Commentarii Mathematici Helvetici, vol. 52, no. 4, pp. 591–602, 1977. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  16. K. H. Zhu, Operator Theory in Function Spaces, vol. 139 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 1990.
  17. R. Aulaskari, P. Lappan, J. Xiao, and R. Zhao, β€œOn α-Bloch spaces and multipliers of Dirichlet spaces,” Journal of Mathematical Analysis and Applications, vol. 209, no. 1, pp. 103–121, 1997. View at Publisher Β· View at Google Scholar
  18. D. Walsh, β€œA property of univalent functions in Ap,” Glasgow Mathematical Journal, vol. 42, no. 1, pp. 121–124, 2000. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  19. J. J. Donaire, D. Girela, and D. Vukotić, β€œOn univalent functions in some Möbius invariant spaces,” Journal für die Reine und Angewandte Mathematik, vol. 553, pp. 43–72, 2002. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  20. J. Xiao, Holomorphic Q Classes, vol. 1767 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2001. View at Publisher Β· View at Google Scholar
  21. J. Xiao, Geometric Qp Functions, Frontiers in Mathematics, Birkhäuser, Basel, Switzerland, 2006. View at Zentralblatt MATH
  22. M. Essén and H. Wulan, β€œOn analytic and meromorphic functions and spaces of QK-type,” Illinois Journal of Mathematics, vol. 46, no. 4, pp. 1233–1258, 2002. View at Google Scholar
  23. M. Essén, H. Wulan, and J. Xiao, β€œSeveral function-theoretic characterizations of Möbius invariant QK spaces,” Journal of Functional Analysis, vol. 230, no. 1, pp. 78–115, 2006. View at Google Scholar Β· View at Zentralblatt MATH
  24. H. Wulan and P. Wu, β€œCharacterizations of QT spaces,” Journal of Mathematical Analysis and Applications, vol. 254, no. 2, pp. 484–497, 2001. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  25. M. Pavlović and J. A. Peláez, β€œAn equivalence for weighted integrals of an analytic function and its derivative,” Mathematische Nachrichten, vol. 281, no. 11, pp. 1612–1623, 2008. View at Publisher Β· View at Google Scholar
  26. H. Wulan, β€œMultivalent functions and QK spaces,” International Journal of Mathematics and Mathematical Sciences, no. 45–48, pp. 2537–2546, 2004. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH