Geodesic
On the theorems of Beurling, Carleson and Tsuji on exceptional sets
Sbornik. Mathematics, Tome 23 (1974) no. 1, pp. 1-12 
V. I. Gavrilov. On the theorems of Beurling, Carleson and Tsuji on exceptional sets. Sbornik. Mathematics, Tome 23 (1974) no. 1, pp. 1-12. http://geodesic.mathdoc.fr/item/SM_1974_23_1_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper consists of two parts. In the first part, a general theorem is proved on the behavior along chords of functions defined on the unit disk, and this theorem is applied to continuous functions of bounded type. In the second part, boundary uniqueness theorems are proved for functions meromorphic in the unit disk. Bibliography: 12 titles.

[1] A. Beurling, “Ensembles exceptionnels”, Acta Math., 72 (1940), 1–13 | DOI | MR | Zbl

[2] A. Broman, “On two classes of trigonometrical series”, Thesis, Univ. Uppsala, 1947, 1–51 | MR

[3] V. I. Gavrilov, “Povedenie vdol khord funktsii, opredelennykh v edinichnom kruge”, Summaries, Third Cong. Bulgarian Math. (Varna, Sept. 6–15), 1972, 34

[4] V. S. Zakharyan, “O segmentnom izmenenii odnogo klassa analiticheskikh funktsii”, Izv. AN Arm. SSR, seriya matem., 2:2 (1967), 117–122 | MR | Zbl

[5] G. T. Cargo, “The segmental variation of Blaschke products”, Duke Math. J., 30 (1963), 143–149 | DOI | MR | Zbl

[6] L. Carleson, “On a class of meromorphic functions and its exceptional sets”, Thesis, Univ. Uppsala, 1950, 1–46 | MR

[7] L. Karleson, Izbrannye problemy teorii isklyuchitelnykh mnozhestv, izd-vo «Mir», Moskva, 1971 | MR

[8] E. Kollingvud, A. Lovater, Teoriya predelnykh mnozhestv, izd-vo «Mir», Moskva, 1971 | MR

[9] R. Nevanlinna, Odnoznachnye analiticheskie funktsii, Gostekhizdat, Moskva–Leningrad, 1941 | MR

[10] I. I. Privalov, Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, Moskva–Leningrad, 1950

[11] W. Rudin, “The radial variation of analytic functions”, Duke Math. J., 22 (1955), 235–242 | DOI | MR | Zbl

[12] M. Tsuji, “Beurling's theorem on exceptional sets”, Tôhoku Math. J., 2 (1950), 113–125 | DOI | MR | Zbl