On Logarithmic Derivatives of Functions in a Class of Starlike Mappings
Canadian mathematical bulletin, Tome 36 (1993) no. 1, pp. 38-44

Voir la notice de l'article provenant de la source Cambridge University Press

The purpose of this paper is to prove some facts about integral means of (d2/dz2)(log[f(z)/z])—or equivalently f′′/f, for f in a class of starlike mappings of a "singular" nature. In particular it is noted that the Koebe function is not extremal for the Hardy means Mp(r,f′′/f) for functions in this class.
DOI : 10.4153/CMB-1993-007-1
Mots-clés : 30C45
Gluchoff, Alan D. On Logarithmic Derivatives of Functions in a Class of Starlike Mappings. Canadian mathematical bulletin, Tome 36 (1993) no. 1, pp. 38-44. doi: 10.4153/CMB-1993-007-1
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[1] 1. Ahern, P., The Mean Modulus and the Derivative of an Inner Function, Indiana University Mathematics Journal (2) 28(1979), 311–347. Google Scholar

[2] 2. Ahern, P., The Poisson Integral of a Singular Measure, Canad. J. Math. XXXV(1983), 735–749. Google Scholar

[3] 3. Ahern, P. and Clark, D., On Inner Functions With Hp Derivative, Michigan Math J. 21(1974), 115–127. Google Scholar

[4] 4. Caughren, J. G. and Shields, A., Singular Inner Factors of Analytic Functions, Michigan Math. J. 16(1969), 409–410. Google Scholar

[5] 5. Cullen, M. R., Derivatives of Singular Inner Functions, Michigan Math J. 18(1971), 283–287. Google Scholar

[6] 6. Duren, P. L., Theory of H Spaces, Academic Press, New York, 1970. Google Scholar

[7] 7. Duren, P. L., Univalent Functions, Springer-Verlag, New York and Heidelberg, 1983. Google Scholar

[8] 8. Duren, P. L. and Y Leung, J., Logarithmic Coefficients of Univalent Functions, Journal d'Analyse Mathématique 36(1979), 36–43. Google Scholar

[9] 9. Elhosh, M. M., On Integral Means of Derivatives of Univalent Functions, Bull. Korean Math. Soc. (1) 24(1987), 13–17. Google Scholar

[10] 10. Feng, J. and MacGregor, T. H., Estimates on Integral Means of the Derivatives of Univalent Functions, Notices Amer. Math. Soc. 21 August (1974), A-492. Google Scholar

[11] 11. Garnett, J., Bounded Analytic Functions, Academic Press, New York, 1981. Google Scholar

[12] 12. Keogh, F. R., Conformai Mappings of Bounded Star-Shaped Domains, Proc. London Math Society (3) 9(1959), 481–491. Google Scholar

[13] 13. MacGregor, T. H., Applications of Extreme Point Theory To Univalent Functions, Michigan Math J. (4) 19(1972), 361–376. Google Scholar

[14] 14. Pommerenke, C., On Starlike and Convex Functions, J. London Math. Soc. 37(1962), 209–224. Google Scholar

[15] 15. Sheil-Small, T., Starlike Univalent Functions, Proc. London Math. Soc. (3) 21(1970), 577–613. Google Scholar

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