Abstract
In this article we derive new estimates for the moduli of the Taylor coefficients of Bloch functions. We use one of these estimates to prove an inequality of an area type for such functions.
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References
F. G. Avkhadiev and I. R. Kayumov, “Estimates for Bloch functions and their generalization,” Dokl. Akad. Nauk 349, 583–585 (1996).
M. Bonk, PhD Dissertation (TU Braunschweig, 1988).
P. Duren, Univalent Functions (Springer, Berlin, New York, Heidelberg, 1983).
O. V. Ivrii and I. R. Kayumov, “Makarov’s principle for the Bloch unit ball,” Sb. Math. 208, 399–412 (2017).
I. R. Kayumov, “A note on an area type functional of Bloch functions,” Lobachevskii J. Math. 33 (3), 464–468 (2017).
I. R. Kayumov and K.-J. Wirths, “Coefficient problems for Bloch functions,” Anal. Math. Phys. (2019, in press).
E. Landau, “Über die Bloch’sche Konstante und zwei verwandte Weltkonstanten,” Math. Z. 30, 608–634 (1929).
“Research Problems,” Bull. Am. Math. Soc. 71, 853–857 (1965).
K.-J. Wirths, “Über holomorphe Functionen, die einer Wachstumsbeschränkung unterliegen,” Arch. Math. 30, 606–612 (1978).
Funding
The research of I. Kayumov was supported by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities (1.9773.2017/8.9) and by Russian Foundation for Basic Research, project no. 17-01-00282.
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Kayumov, I.R., Wirths, KJ. Coefficient Inequalities for Bloch Functions. Lobachevskii J Math 40, 1319–1323 (2019). https://doi.org/10.1134/S1995080219090117
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DOI: https://doi.org/10.1134/S1995080219090117