Duke Mathematical Journal

On coefficient problems for univalent functions and conformal dimension

Lennart Carleson and Peter W. Jones

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J. Volume 66, Number 2 (1992), 169-206.

Dates
First available: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077294777

Mathematical Reviews number (MathSciNet)
MR1162188

Zentralblatt MATH identifier
0765.30005

Digital Object Identifier
doi:10.1215/S0012-7094-92-06605-1

Subjects
Primary: 30C50: Coefficient problems for univalent and multivalent functions
Secondary: 30C85: Capacity and harmonic measure in the complex plane [See also 31A15] 30D05: Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX]

Citation

Carleson, Lennart; Jones, Peter W. On coefficient problems for univalent functions and conformal dimension. Duke Mathematical Journal 66 (1992), no. 2, 169--206. doi:10.1215/S0012-7094-92-06605-1. http://projecteuclid.org/euclid.dmj/1077294777.


Export citation

References

  • [1] A. Beurling, The collected works of Arne Beurling. Vol. 2, Contemporary Mathematicians, Birkhäuser Boston Inc., Boston, MA, 1989.
  • [2] L. de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), no. 1-2, 137–152.
  • [3] R. Bowen, Hausdorff dimension of quasicircles, Inst. Hautes Études Sci. Publ. Math. (1979), no. 50, 11–25.
  • [4] L. Carleson, On the support of harmonic measure for sets of Cantor type, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 113–123.
  • [5] J. Clunie and Ch. Pommerenke, On the coefficients of univalent functions, Michigan Math. J. 14 (1967), 71–78.
  • [6]1 A. Douady and J. H. Hubbard, Étude dynamique des polynômes complexes. Partie I, Publications Mathématiques d'Orsay [Mathematical Publications of Orsay], vol. 84, Université de Paris-Sud, Département de Mathématiques, Orsay, 1984.
  • [6]2 A. Douady and J. H. Hubbard, Étude dynamique des polynômes complexes. Partie II, Publications Mathématiques d'Orsay [Mathematical Publications of Orsay], vol. 85, Université de Paris-Sud, Département de Mathématiques, Orsay, 1985.
  • [7] A. Douady and J. H. Hubbard, On the dynamics of polynomial-like mappings, Ann. Sci. École Norm. Sup. (4) 18 (1985), no. 2, 287–343.
  • [8] P. L. Duren, Univalent functions, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 259, Springer-Verlag, New York, 1983.
  • [9] U. Frisch and G. Parisi, in Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, Proc. Internat. School of Phys. “Enrico Fermi” ed. M. Ghill, vol. 88, North-Holland, Amsterdam, 1985, p. 84.
  • [10] J. Garnett, Bounded Analytic Functions, Academic, New York, 1983.
  • [11] P. Grassberger and I. Procaccia, Measuring the strangeness of strange attractors, Phys. D 9 (1983), no. 1-2, 189–208.
  • [12] T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman, Fractal measures and their singularities: the characterization of strange sets, Phys. Rev. A (3) 33 (1986), no. 2, 1141–1151.
  • [13] H. G. E. Hentschel and I. Procaccia, The infinite number of generalized dimensions of fractals and strange attractors, Phys. D 8 (1983), no. 3, 435–444.
  • [14] N. G. Makarov, On the distortion of boundary sets under conformal mappings, Proc. London Math. Soc. (3) 51 (1985), no. 2, 369–384.
  • [15] B. B. Mandelbrot, Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier, J. Fluid Mech. 62 (1974), 331–358.
  • [16] O. Martio and J. Sarvas, Injectivity theorems in plane and space, Ann. Acad. Sci. Fenn. Ser. A I Math. 4 (1979), no. 2, 383–401.
  • [17] Ch. Pommerenke, On the integral means of the derivative of a univalent function. II, Bull. London Math. Soc. 17 (1985), no. 6, 565–570.
  • [18] C. Pommerenke, Univalent functions, Vandenhoeck & Ruprecht, Göttingen, 1975.
  • [19] D. Ruelle, Repellers for real analytic maps, Ergodic Theory Dynamical Systems 2 (1982), no. 1, 99–107.
  • [20] D. Sullivan, Quasiconformal homeomorphisms and dynamics. I. Solution of the Fatou-Julia problem on wandering domains, Ann. of Math. (2) 122 (1985), no. 3, 401–418.
  • [21] A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959.
  • [22] A. Zygmund, On certain lemmas of Marcinkiewicz and Carleson, J. Approximation Theory 2 (1969), 249–257.