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On a Blaschke-type condition for the zeros of derivatives of R. Nevanlinna class functions in the disk. (English. Russian original) Zbl 1535.30124

St. Petersbg. Math. J. 34, No. 6, 1063-1072 (2023); translation from Algebra Anal. 34, No. 6, 228-241 (2022).
Summary: A necessary and sufficient Blaschke-type condition is obtained for the zeros of derivatoves of Nevanlinna class functions.

MSC:

30H10 Hardy spaces
30H15 Nevanlinna spaces and Smirnov spaces
30H35 BMO-spaces
Full Text: DOI

References:

[1] A. V. Aleksandrov and V. V. Peller, Hankel operators and similarity to a contraction, Internat. Math. Res. Notices 1996, no.6, 263-275. 1386078 · Zbl 0871.47025
[2] W. S. Cohn and I. E. Verbitsky, Factorization of tent spaces and Hankel operators, J. Funct. Anal. 175 (2000), no. 2, 308-329. 1780479 · Zbl 0968.46022
[3] R. M. Dyakonov, Factoring derivatives of functions in the Nevanlinna and Smirnov classes, Ann. Acad. Sci. Fenn. Math. 37 (2012), no. 2, 407-413. 2987075 · Zbl 1266.30048
[4] A. E. Djrbashian and F. A. Shamoyan, Topics in the theory of \(A^p_\) spaces, Teubner-Texte Math., vol. 105, BSB B. G. Teubner Verlagsgesellschaft, Leipzig, 1988. 1021691 · Zbl 0667.30032
[5] H. Hedenmalm, B. Korenblum, and K. Zhu, Theory of Bergman spaces, Grad. Texts in Math., vol. 199, Springer, New York, 2000. 1758653 · Zbl 0955.32003
[6] D. Ullrich, Khinchin’s inequality and the zeroes of Bloch functions, Duke Math. J. 57 (1988), no. 2, 519-535. 962518 · Zbl 0678.30006
[7] M. M. Djrbashian, Representation problem for analytic functions, Soobshch. Inst. Mat. Mekh. AN Arm.SSR 3 (1948), 3-40. (Russian)
[8] W. K. Hayman, Meromorphic functions, Oxford Math. Monogr., Clarendon Press, Oxford, 1964. 164038 · Zbl 0115.06203
[9] N. Bourbaki, Elements de mathematique. IX, Fonctions d’une variable reelle. Theorie elementaire, Actualites Sci. Industr., No. 1074, Hermann, Paris, 1949. 31013 · Zbl 0036.16801
[10] F. A. Shamoyan and I. S. Kursina, On the invariance of some classes of holomorphic functions with respect to integrodifferential operators, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 255 (1998), 184-197; English transl., J. Math. Sci. (N. Y.) 107 (2001), no. 4, 4097-4107. 1692904 · Zbl 1134.30326
[11] F. A. Shamoyan, Description of closed ideals and certain factorization questions in algebras of growing functions that are analytic in the disc, Izv. Akad. Nauk Armjan. SSR Ser. Mat. 5 (1970), no. 5, 419-433. (Russian) 291815 · Zbl 0219.30039
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