Geodesic
Paley problem for plurisubharmonic functions of finite lower order
Sbornik. Mathematics, Tome 190 (1999) no. 2, pp. 309-321 Cet article a éte moissonné depuis la source Math-Net.Ru

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For plurisubharmonic functions $\mathbb C^n$ of lower order $\lambda<+\infty$ estimates of the growth of their maximum value on the sphere of radius $r$ with centre at the origin in terms of the growth of the Nevanlinna characteristics $T(r,u)$ are obtained. These estimates are best possible for $\lambda\leqslant 1$. The results are new even in the case of functions of the form $u=\log|f|$, where $f$ is an entire function in $\mathbb C^n$, $n>1$. 
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     author = {B. N. Khabibullin},
     title = {Paley problem for plurisubharmonic functions of finite lower order},
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     pages = {309--321},
     year = {1999},
     volume = {190},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1999_190_2_a6/}
}
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B. N. Khabibullin. Paley problem for plurisubharmonic functions of finite lower order. Sbornik. Mathematics, Tome 190 (1999) no. 2, pp. 309-321. http://geodesic.mathdoc.fr/item/SM_1999_190_2_a6/

[1] Rudin U., Teoriya funktsii v edinichnom share v $\mathbb C^n$, Mir, M., 1984 | MR | Zbl

[2] Govorov N. V., “O gipoteze Peili”, Funkts. analiz i ego prilozh., 3:2 (1969), 41–45 | MR | Zbl

[3] Petrenko V. P., “Rost meromorfnykh funktsii konechnogo nizhnego poryadka”, Izv. AN SSSR. Ser. matem., 33 (1969), 414–454 | MR | Zbl

[4] Dahlberg B., “Mean values of subharmonic functions”, Ark. Mat., 10 (1972), 293–309 | DOI | MR | Zbl

[5] Sodin M. L., O roste v metrike $L^p$ tselykh funktsii konechnogo nizhnego poryadka, Dep. v Ukr. NIINTI 02.07.83, No 420. Uk–D 83

[6] Kondratyuk A. A., Tarasyuk S. I., Vasyl'kiv Ya. V., “General Paley Problem”, Ukr. matem. zhurn., 48:1 (1996), 25–34 | MR

[7] Khabibullin B. N., “Problema Peli dlya meromorfnykh v $\mathbb C^n$ funktsii”, Dokl. AN, 342:4 (1995), 461–463 | MR | Zbl

[8] Dzhrbashyan M. M., Integralnye preobrazovaniya i predstavleniya funktsii v kompleksnoi oblasti, Nauka, M., 1966

[9] Khabibullin B. N., “Teorema o naimenshem mazhorante i ee primeneniya. II: Tselye i meromorfnye funktsii konechnogo poryadka”, Izv. RAN. Ser. matem., 57:3 (1993), 70–91 | MR | Zbl

[10] Essén M. R., “The $\cos\pi\lambda$ theorem”, Lecture Notes in Math., 467, 1975, 1–98 | MR

[11] Lavrentev M. A., Shabat B. V., Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1987 | MR | Zbl

[12] Edrei A., “Locally tauberian theorem for meromorphic function of lower order less then one”, Trans. Amer. Math. Soc., 1969, no. 140, 309–332 | DOI | MR | Zbl

[13] Kheiman U., Kennedi P., Subgarmonicheskie funktsii, Mir, M., 1980

[14] Khermander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi. T. I. Teoriya raspredelenii i analiz Fure, Mir, M., 1986

[15] Lelon G., Gruman L., Tselye funktsii mnogikh kompleksnykh peremennykh, Nauka, M., 1989

[16] Govorov N. V., Kraevaya zadacha Rimana s beskonechnym indeksom, Nauka, M., 1986 | MR | Zbl

[17] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, T. I, Nauka, M., 1973