Translator Disclaimer
2017 Quasiconformal extendability of integral transforms of Noshiro-Warschawski functions
Ikkei Hotta, Li-Mei Wang
Rocky Mountain J. Math. 47(1): 185-204 (2017). DOI: 10.1216/RMJ-2017-47-1-185

Abstract

Since the nonlinear integral transforms $$ J_{\alpha }[f](z) = \int _{0}^{z}(f'(u))^{\alpha } du $$ and $$ \ \ I_{\alpha }[f](z) =\int _0^z (f(u)/u)^{\alpha } du $$ with a complex number $\alpha $ were introduced, a great number of studies have been dedicated to deriving sufficient conditions for univalence on the unit disk. However, little is known about the conditions where $J_{\alpha }[f]$ or $I_{\alpha }[f]$ produce a holomorphic univalent function in the unit disk which extends to a quasiconformal map on the complex plane. In this paper, we discuss quasiconformal extendability of the integral transforms $J_{\alpha }[f]$ and $I_{\alpha }[f]$ for holomorphic functions which satisfy the Noshiro-Warschawski criterion. Various approaches using pre-Schwarzian derivatives, differential subordination and Loewner theory are applied to this problem.

Citation

Download Citation

Ikkei Hotta. Li-Mei Wang. "Quasiconformal extendability of integral transforms of Noshiro-Warschawski functions." Rocky Mountain J. Math. 47 (1) 185 - 204, 2017. https://doi.org/10.1216/RMJ-2017-47-1-185

Information

Published: 2017
First available in Project Euclid: 3 March 2017

zbMATH: 06702341
MathSciNet: MR3619760
Digital Object Identifier: 10.1216/RMJ-2017-47-1-185

Subjects:
Primary: 30C45, 30C62, 44A15

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

JOURNAL ARTICLE
20 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.47 • No. 1 • 2017
Back to Top