A note on an area-type functional of Bloch functions
- Authors: Kayumov I.R.1
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Affiliations:
- N.I. Lobachevskii Institute ofMathematics and Mechanics
- Issue: Vol 38, No 3 (2017)
- Pages: 466-468
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/199248
- DOI: https://doi.org/10.1134/S1995080217030155
- ID: 199248
Cite item
Abstract
Let D be the unit disk centered at the origin in the complex plane. In this paper we consider an extremal problem for an area-type functional in the space B of Bloch functions with the seminorm ||b||B = sup{(1 − |z|2)|b’(z)|: z ∈ D}. We show that sup{Σk=1n k|bk|2: ||b||B ≤ 1} = nBn2, n = 1, 2, 3, 4, 5, where bk are the Taylor coefficients of b and Bn = sup{|bn|: ||b||B ≤ 1}.
Keywords
About the authors
I. R. Kayumov
N.I. Lobachevskii Institute ofMathematics and Mechanics
Author for correspondence.
Email: ikayumov@gmail.com
Russian Federation, Kremlevskaya ul. 35, Kazan, Tatarstan, 420008