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Analogues to Landau’s inequality for nonvanishing bounded functions and for Bloch functions. (English) Zbl 1421.30074

Summary: Starting with some famous inequalities for unimodular bounded functions proved by E. Landau and O. Szász, we derive similar inequalities for Bloch functions and unimodular bounded and nonvanishing functions.

MSC:

30H30 Bloch spaces
30H05 Spaces of bounded analytic functions of one complex variable
30B10 Power series (including lacunary series) in one complex variable
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References:

[1] Anderson, J.M., Clunie, J., Pommerenke, Ch.: On Bloch functions and normal functions. J. Reine Angew. Math. 270, 12-37 (1974) · Zbl 0292.30030
[2] Fejér, L.: Über gewisse durch die Fouriersche und Laplacesche Reihe definierten Mittelkurven und Mittelflächen. Rend. Circolo Mat. Palermo 38, 79-97 (1914) · JFM 45.0412.03
[3] Landau, L.: Abschätzung der Koeffizientensumme einer Potenzreihe. Arch. Math. Physik 21, 250-255 (1913) · JFM 44.0288.03
[4] Lewandowski, Z., Szynal, J.: The Landau problem for bounded nonvanishing functions. J. Comput. Appl. Math. 105, 367-369 (1999) · Zbl 0945.30011
[5] Landau, L., Gaier, D.: Darstellung und Begründung einiger neuerer Ergebnisse der Funktionentheorie, 3rd edn. Springer, Berlin (1986) · Zbl 0601.30001
[6] Martin, M.J., Sawyer, E.T., Uriarte-Tuero, I., Vukotić, D.: The Krzyż conjecture revisited. Adv. Math. 273, 716-745 (2015) · Zbl 1310.30045
[7] Szász, O.: Ungleichungen für die Koeffizienten einer Potenzreihe. Math. Z. 1, 163-183 (1918) · JFM 46.0479.01
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