Nonbasic harmonic maps onto convex wedges
Cima, Josephi ; Livingston, Alberti
Colloquium Mathematicae, Tome 66 (1993), p. 9-22 / Harvested from The Polish Digital Mathematics Library

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

Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:210239
@article{bwmeta1.element.bwnjournal-article-cmv66i1p9bwm,
     author = {Josephi Cima and Alberti Livingston},
     title = {Nonbasic harmonic maps onto convex wedges},
     journal = {Colloquium Mathematicae},
     volume = {66},
     year = {1993},
     pages = {9-22},
     zbl = {0820.30015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv66i1p9bwm}
}
Cima, Josephi; Livingston, Alberti. Nonbasic harmonic maps onto convex wedges. Colloquium Mathematicae, Tome 66 (1993) pp. 9-22. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv66i1p9bwm/

[000] [1] Y. Abu-Muhanna and G. Schober, Harmonic mappings onto convex domains, Canad. J. Math. (6) 32 (1987), 1489-1530. | Zbl 0644.30003

[001] [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. | Zbl 0063.00851

[002] [3] J. Cima and A. Livingston, Integral smoothness properties of some harmonic mappings, Complex Variables 11 (1989), 95-110. | Zbl 0724.30011

[003] [4] J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 9 (1984), 3-25. | Zbl 0506.30007

[004] [5] W. Hengartner and G. Schober, On schlicht mappings to domains convex in one direction, Comment. Math. Helv. 45 (1970), 303-314. | Zbl 0203.07604

[005] [6] W. Hengartner and G. Schober, Harmonic mappings with given dilatation, J. London Math. Soc. (2) 33 (1986), 473-483. | Zbl 0626.30018

[006] [7] W. Hengartner and G. Schober, Univalent harmonic functions, Trans. Amer. Math. Soc. 299 (1987), 1-31.

[007] [8] E. Hille, Analytic Function Theory, Vol. II, Ginn, 1962. | Zbl 0102.29401

[008] [9] H. Kneser, Lösung der Aufgabe 41, Jahresber. Deutsch. Math.-Verein. 35 (1926), 123-124. | Zbl 52.0498.03

[009] [10] P. Koosis, Introduction to Hp Spaces, London Math., Soc. Lecture Note Ser. 40, Cambridge University Press, 1980. | Zbl 0435.30001