We construct a nonbasic harmonic mapping of the unit disk onto a convex wedge. This mapping satisfies the partial differential equation where a(z) is a nontrivial extreme point of the unit ball of .
@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 Spaces, London Math., Soc. Lecture Note Ser. 40, Cambridge University Press, 1980. | Zbl 0435.30001