Nonbasic harmonic maps onto convex wedges

Josephi Cima; Alberti Livingston

Colloquium Mathematicae (1993)

  • Volume: 66, Issue: 1, page 9-22
  • ISSN: 0010-1354

Abstract

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We construct a nonbasic harmonic mapping of the unit disk onto a convex wedge. This mapping satisfies the partial differential equation f z ¯ = a f z where a(z) is a nontrivial extreme point of the unit ball of H ∞ .

How to cite

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Cima, Josephi, and Livingston, Alberti. "Nonbasic harmonic maps onto convex wedges." Colloquium Mathematicae 66.1 (1993): 9-22. <http://eudml.org/doc/210239>.

@article{Cima1993,
abstract = {We construct a nonbasic harmonic mapping of the unit disk onto a convex wedge. This mapping satisfies the partial differential equation $\{f_\{\bar\{z\}\}\}=af_\{z\}$ where a(z) is a nontrivial extreme point of the unit ball of $H^∞$.},
author = {Cima, Josephi, Livingston, Alberti},
journal = {Colloquium Mathematicae},
language = {eng},
number = {1},
pages = {9-22},
title = {Nonbasic harmonic maps onto convex wedges},
url = {http://eudml.org/doc/210239},
volume = {66},
year = {1993},
}

TY - JOUR
AU - Cima, Josephi
AU - Livingston, Alberti
TI - Nonbasic harmonic maps onto convex wedges
JO - Colloquium Mathematicae
PY - 1993
VL - 66
IS - 1
SP - 9
EP - 22
AB - We construct a nonbasic harmonic mapping of the unit disk onto a convex wedge. This mapping satisfies the partial differential equation ${f_{\bar{z}}}=af_{z}$ where a(z) is a nontrivial extreme point of the unit ball of $H^∞$.
LA - eng
UR - http://eudml.org/doc/210239
ER -

References

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  1. [1] Y. Abu-Muhanna and G. Schober, Harmonic mappings onto convex domains, Canad. J. Math. (6) 32 (1987), 1489-1530. Zbl0644.30003
  2. [2] G. Choquet, Sur un type de transformation analytique généralisant la représenta- tion conforme et définie au moyen de fonctions harmoniques, Bull. Sci. Math. 69 (1945), 156-165. Zbl0063.00851
  3. [3] J. Cima and A. Livingston, Integral smoothness properties of some harmonic mappings, Complex Variables 11 (1989), 95-110. Zbl0724.30011
  4. [4] J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 9 (1984), 3-25. Zbl0506.30007
  5. [5] W. Hengartner and G. Schober, On schlicht mappings to domains convex in one direction, Comment. Math. Helv. 45 (1970), 303-314. Zbl0203.07604
  6. [6] W. Hengartner and G. Schober, Harmonic mappings with given dilatation, J. London Math. Soc. (2) 33 (1986), 473-483. Zbl0626.30018
  7. [7] W. Hengartner and G. Schober, Univalent harmonic functions, Trans. Amer. Math. Soc. 299 (1987), 1-31. 
  8. [8] E. Hille, Analytic Function Theory, Vol. II, Ginn, 1962. Zbl0102.29401
  9. [9] H. Kneser, Lösung der Aufgabe 41, Jahresber. Deutsch. Math.-Verein. 35 (1926), 123-124. Zbl52.0498.03
  10. [10] P. Koosis, Introduction to H p Spaces, London Math., Soc. Lecture Note Ser. 40, Cambridge University Press, 1980. Zbl0435.30001

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