We construct a nonbasic harmonic mapping of the unit disk onto a convex wedge. This mapping satisfies the partial differential equation $\ov{f_{\bar{z}}}=af_{z}$ where a(z) is a nontrivial extreme point of the unit ball of $H^∞$.
Department of Mathematics, University of Delaware, Newark, Delaware 19711, U.S.A
Bibliografia
[1] Y. Abu-Muhanna and G. Schober, Harmonic mappings onto convex domains, Canad. J. Math. (6) 32 (1987), 1489-1530.
[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.
[3] J. Cima and A. Livingston, Integral smoothness properties of some harmonic mappings, Complex Variables 11 (1989), 95-110.
[4] J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math. 9 (1984), 3-25.
[5] W. Hengartner and G. Schober, On schlicht mappings to domains convex in one direction, Comment. Math. Helv. 45 (1970), 303-314.
[6] W. Hengartner and G. Schober, Harmonic mappings with given dilatation, J. London Math. Soc. (2) 33 (1986), 473-483.
[7] W. Hengartner and G. Schober, Univalent harmonic functions, Trans. Amer. Math. Soc. 299 (1987), 1-31.
[8] E. Hille, Analytic Function Theory, Vol. II, Ginn, 1962.
[9] H. Kneser, Lösung der Aufgabe 41, Jahresber. Deutsch. Math.-Verein. 35 (1926), 123-124.
[10] P. Koosis, Introduction to $H^p$ Spaces, London Math., Soc. Lecture Note Ser. 40, Cambridge University Press, 1980.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv66i1p9bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.