Geodesic
On~some metric properties of the boundary values of functions that are analytic in a~half-plane
Izvestiya. Mathematics , Tome 25 (1985) no. 1, pp. 1-17.

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A generalization is given of Kolmogorov's inequality for the Hilbert transform. The inequalities that are obtained are shown to be exact, and all extremal functions are determined. Bibliography: 9 titles. 
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N. V. Govorov; S. P. Grushevskii. On~some metric properties of the boundary values of functions that are analytic in a~half-plane. Izvestiya. Mathematics , Tome 25 (1985) no. 1, pp. 1-17. http://geodesic.mathdoc.fr/item/IM2_1985_25_1_a0/

[1] Tsereteli O. D., “Metricheskie svoistva sopryazhennykh funktsii”, Sovremennye problemy matematiki, 7, M., 1975, 18–57

[2] Tsereteli O. D., “Zamechanie o sopryazhennykh funktsiyakh”, Soobsch. ANGruz. SSR, 63:1 (1971), 42–44

[3] Tsereteli O. D., “Zamechanie k teoremam Kolmogorova i F. i M. Rissov”, Tr. Simpoz. po mekhanike sploshnoi sredy i rodstvennykh problem analiza, v. 1 (1971), Metsniereba, Tbilisi, 1973, 241–254

[4] Tsereteli O. D., “O sopryazhennykh funktsiyakh”, Matem. zametki, 22:5 (1977), 171–183

[5] Govorov I. V., Grushevskii S. P., “O nekotorykh metricheskikh svoistvakh granichnykh znachenii funktsii, analiticheskikh v poluploskosti”, Dokl. AN SSSR, 242:1 (1978), 21–24 | MR | Zbl

[6] Akhiezer N. I., Glazman I. M., Teoriya lineinykh operatorov v gilbertovom prostranstve, Vischa shkola, Kharkov, 1977

[7] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, GITTL, M., L., 1950

[8] Kollingvud E., Lovater L., Teoriya predelnykh mnozhestv, Mir, M., 1971 | MR

[9] Macintyre A. J., Fuchs W. H. J., “Inequalities for the logarithmic derivatives of a polinomial”, J. London Math. Soc., 15 (1940) | DOI | MR | Zbl