Geodesic
Boundary Behavior of Analytic Riesz Products in the~Disk
Matematičeskie trudy, Tome 9 (2006) no. 1, pp. 34-51.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study a fractal-type class of conformal mappings and formulate for it a criterion of almost everywhere existence of the angular limits of the derivatives in terms of the moduli of the coefficients of the logarithm of the derivative. Moreover, we establish a connection between the asymptotic variance and spectrum of the integral means of these mappings. 
@article{MT_2006_9_1_a2,
     author = {I. R. Kayumov},
     title = {Boundary {Behavior} of {Analytic} {Riesz} {Products} in {the~Disk}},
     journal = {Matemati\v{c}eskie trudy},
     pages = {34--51},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2006_9_1_a2/}
}
TY  - JOUR
AU  - I. R. Kayumov
TI  - Boundary Behavior of Analytic Riesz Products in the~Disk
JO  - Matematičeskie trudy
PY  - 2006
SP  - 34
EP  - 51
VL  - 9
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2006_9_1_a2/
LA  - ru
ID  - MT_2006_9_1_a2
ER  - 
%0 Journal Article
%A I. R. Kayumov
%T Boundary Behavior of Analytic Riesz Products in the~Disk
%J Matematičeskie trudy
%D 2006
%P 34-51
%V 9
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2006_9_1_a2/
%G ru
%F MT_2006_9_1_a2
I. R. Kayumov. Boundary Behavior of Analytic Riesz Products in the~Disk. Matematičeskie trudy, Tome 9 (2006) no. 1, pp. 34-51. http://geodesic.mathdoc.fr/item/MT_2006_9_1_a2/

[1] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR

[2] Zigmund A., Trigonometricheskie ryady, t. 1, Mir, M., 1965 | MR

[3] Markushevich A. I., “Nekotorye voprosy teorii granichnykh svoistv analiticheskikh funktsii”, Uspekhi mat. nauk, 4:4(32) (1949), 3–18 | MR | Zbl

[4] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, Gostekhizdat, M.; L., 1950

[5] Khardi G., Littlvud D., Polia G., Neravenstva, Izd-vo inostr. lit., M., 1948

[6] Hamilton D. N., “Length of Julia curves”, Pacific J. Math., 169:1 (1995), 75–93 | MR | Zbl

[7] Kayumov I. R., “The law of the iterated logarithm for locally univalent functions”, Ann. Acad. Sci. Fenn. Math., 27:2 (2002), 357–364 | MR | Zbl

[8] Littlewood J., “On the coefficients of schlicht functions”, Quart. J. Math. Oxford Ser. (2), 9 (1938), 14–20 | DOI | MR | Zbl

[9] Makarov N. G., “Fine structure of harmonic measure”, St. Petersburg Math. J., 10:2 (1999), 217–268 | MR

[10] Pommerenke Ch., “On Bloch functions”, J. London Math. Soc. (2), 2 (1970), 689–695 | MR | Zbl

[11] Pommerenke Ch., Boundary Behavior of Conformal Maps, Fundamental Principles of Mathematical Sciences, Springer-Verlag, Berlin, 1992 | MR | Zbl

[12] Przytycki F., Urbanski M., and Zdunik A., “Harmonic, Gibbs, and Hausdorff measures on repellers for holomorphic maps. I, II”, Ann. of Math. (2), 130:1 (1989), 1–40 ; Studia Math., 97:3 (1991), 189–225 | DOI | MR | Zbl | MR | Zbl