Geodesic
On the differentiation in the Privalov classes
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 5, pp. 622-630.

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The invariance of the Privalov classes with respect to the differentiation operator is studied.
Keywords: Privalov spaces, the Bloch–Nevanlinna conjecture, differentiation operator. 
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Eugenia G. Rodikova; Faizo A. Shamoyan. On the differentiation in the Privalov classes. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 5, pp. 622-630. http://geodesic.mathdoc.fr/item/JSFU_2020_13_5_a9/

[1] D. Campbell, G. Wickes, “The Bloch–Nevanlinna conjecture revisited”, Bull. Austral. Math. Soc., 18 (1978), 447–453 | DOI | MR | Zbl

[2] M.M. Djrbashian, “On the problem of the representation of analytic functions”, Soobshch. inst. matem. i mehan. Acad. Nauk Arm. SSR, 2 (1948), 3–40 (in Russian)

[3] P.L. Duren, “On the Bloch-Nevanlinna conjecture”, Colloq. Math., 20 (1969), 295–297 | DOI | MR | Zbl

[4] P.L. Duren, Theory of $H^p$ spaces, Pure and Appl. Math., 38, Academic Press, NY, 1970 | MR

[5] O. Frostman, “Sur les produits des Blaschke”, Kungl. Fysiografiska Sallskapets i Lund Forhandlingar [Proa. Roy. Physiog. Soa. Lund], 12:15 (1942), 169–182 | MR | Zbl

[6] V.I. Gavrilov, A.V. Subbotin, D.A. Efimov, Boundary properties of analytic functions (further contribution), Publishing House of the Moscow University, M., 2012 (in Russian) | MR

[7] G. Hardy, J. Littlewood, G. Polia, Inequalities, Translate from English V. I. Levin (transl.), eds. S. B. Stechkin, GITTL, M., 1948 | MR

[8] W.K. Hayman, “On the characteristics of functions meromorphic in the unit disk and of their integrals”, Acta. math., 112:3–4 (1964), 181–214 | DOI | MR

[9] R. Nevanlinna, Le theoreme de Picard-Borel et la theorie des fonctions meromorphes, Gauthiers-Villars, Paris, 1929 | MR | Zbl

[10] R. Nevanlinna, Eindeutige analytische Funktionen, 2nd ed., Springer-Verlag, Berlin, 1953 | MR | Zbl

[11] I.I. Privalov, Boundary properties of single-valued analytic functions, Izd. Moscow State University, M., 1941 (in Russian) | MR

[12] I.I. Privalov, Boundary properties of analytic functions, GITTL, M.–L., 1950 (in Russian) | MR

[13] E.G. Rodikova, “Coefficient multipliers for the Privalov classes in a disk”, J. Sib. Fed. Univ. Math. Phys., 11:6 (2018), 723–732 | DOI | MR

[14] E.G. Rodikova, V.A. Bednazh, “On interpolation in the Privalov classes in a disk”, Sib. electronic matem. reports, 16 (2019), 1762–1775 (in Russian) | Zbl

[15] E.G. Rodikova, “On properties of zeros of functions from the Privalov class in a disk”, Scientific notes of Bryansk State Univ., 2019, no. 4, 19–22 (in Russian)

[16] E.G. Rodikova, “On interpolation sequences in the Privalov spaces”, Complex analysis, mathematical physics and nonlinear equations, collection of abstracts of the International Scientific Conference (Ufa, 2020), 52–53 (in Russian) | MR

[17] F.A. Shamoyan, “Factorization theorem M. M. Djrbashian and characterization of zeros of analytic functions with a majorant of finite growth”, Izv. Acad. nauk Arm. SSR, Matem., 13:5–6 (1978), 405–422 (in Russian) | MR | Zbl

[18] F.A. Shamoyan, “Parametric representation and description of the root sets of weighted classes of functions holomorphic in the disk”, Siberian Math. J., 40:6 (1999), 1211–1229 | DOI | MR | Zbl

[19] F.A. Shamoyan, Weighted spaces of analytic functions with a mixed norm, Bryansk St. Univ., Bryansk, 2014 (in Russian)

[20] F.A. Shamoyan, “On some properties of zero sets of the Privalov class in a disk”, Zap. nauch. semin. POMI, 480, 2019, 199–205 (in Russian)

[21] F.A. Shamoyan, I.S. Kursina, “On the invariance of some classes of holomorphic functions under integral and differential operators”, J. Math. Sci. (New York), 107:4 (2001), 4097–4107 | DOI | MR

[22] S.V. Shvedenko, “Hardy classes and the spaces of analytic functions associated with them in the unit disc, polydisc, and ball”, Itogi Nauki i Tekhniki. Ser. Mat. Anal., 23, 1985, 3–124 (in Russian) | MR | Zbl