This is a preview of subscription content, log in via an institution to check access.
References
[Br] J. Brennan,The integrability of the derivative in conformal mapping, J. London Math. Soc.18 (1978), 261–272.
[FHM] J. L. Fernández, J. Heinonen and O. Martio,Quasilines and conformal mappings, J. Analyse Math.52 (1989), 117–132.
[GGJ] J. Garnett, F. Gehring and P. Jones,Conformally invariant length sums, Indiana Univ. Math. J.32 (1983), 809–824.
[Ha] V. P. Havin et al., eds.,Linear and Complex Analysis Problem Book, Lecture Notes in Math.1043, Springer-Verlag, Berlin, 1984.
[HW] W. K. Hayman and J-M. G. Wu,Level sets of univalent functions, Comment. Math. Helv.56 (1981), 366–403.
[He] P. Henrici,Applied and Computational Complex Analysis, Vol. III, Wiley, New York, 1986.
[LV] O. Lehto and K. Virtanen,Quasiconformal Mappings in the Plane, Springer-Verlag, New York, 1973.
[M] N. G. Makarov,Metric properties of harmonic measure, Proceedings of the 1986 I.C.M. Vol. I, 766–776, A.M.S., 1987.
[P1] Ch. Pommerenke,On the integral means of the derivative of a univalent function, J. London Math. Soc.32 (1985), 254–258.
[P2] Ch. Pommerenke,The growth of the derivative of a univalent function, inThe Bieberbach Conjecture, A. Baernstein et al., eds., A.M.S., 1986, pp 143–152.
[T] L. N. Trefethen,Numerical computation of the Schwarz-Christoffel transformation, SIAM J. Sci. Stat. Comput.1 (1980), 82–102.
[W] T. Wolff,Counterexamples with harmonic gradient in R 3, preprint, Courant Institute.
Author information
Authors and Affiliations
Additional information
This research was supported by a grant from the National Science Foundation.
Rights and permissions
About this article
Cite this article
Baernstein, A. A counterexample concerning integrability of derivatives of conformal mappings. J. Anal. Math. 53, 253–268 (1989). https://doi.org/10.1007/BF02793417
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02793417