On a Theorem of Nehari and Quasidiscs
نویسندگان
چکیده
Let f be a locally injective analytic map of the unit disc D and let ff; zg be its Schwarzian derivative. Suppose jff; zgj 2p(jzj). We use the classical connection between Schwarzian derivative and second order linear equations to show that, for a particular class of functions p , the image f (D) is a quasidisc. The analysis centers on the diierential equation y 00 + py = 0 and a niteness condition of a positive solution y. The proofs are based on Sturm comparison theorems. When p in the class is analytic and x = 1 is a regular singular point of the linear equation, it is possible to obtain precise information about HH older continuity of f from considerations on the Frobenius solutions at that point. The main result in this paper resolves the complementary case in a general theorem of univalence of Nehari.
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