On the Phragmen–Lindelof principle for subharmonic functions
Izvestiya. Mathematics, Tome 63 (1999) no. 2, pp. 401-422
Cet article a éte moissonné depuis la source Math-Net.Ru
We consider subharmonic functions $f(z)$ in a domain $D\subset\mathbb C$ such that $f(z)$ does not exceed some constant $C$ at all points of $\partial D\setminus\zeta$, $\zeta\in\partial D$. Theorems of Phragmen–Lindelof type provide an upper bound (depending on the structure of the domain $D$) for the a priori possible growth of $f(z)$ as $z\to\zeta$ such that functions satisfying this estimate do not exceed $C$ in the whole domain $D$. We obtain a Phragmen–Lindelof type theorem in which the restriction on the possible growth of $f(z)$ as $z\to\zeta$ is expressed in terms of the lower density (with respect to plane Lebesgue measure) of the set $\mathbb C\setminus D$ at the point $\zeta$.
@article{IM2_1999_63_2_a5,
author = {D. S. Telyakovskii},
title = {On the {Phragmen{\textendash}Lindelof} principle for subharmonic functions},
journal = {Izvestiya. Mathematics},
pages = {401--422},
year = {1999},
volume = {63},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1999_63_2_a5/}
}
D. S. Telyakovskii. On the Phragmen–Lindelof principle for subharmonic functions. Izvestiya. Mathematics, Tome 63 (1999) no. 2, pp. 401-422. http://geodesic.mathdoc.fr/item/IM2_1999_63_2_a5/
[1] Privalov I. I., Subgarmonicheskie funktsii, ONTI, M.–L., 1937
[2] Telyakovskii D. S., “Ob odnoi teoreme tipa Fragmena–Lindelefa dlya subgarmonicheskikh funktsii”, Mezhdunarodnaya konferentsiya “Funktsionalnye prostranstva, teoriya priblizhenii, nelineinyi analiz”, Tez. dokl., MIAN, M., 1995, 267
[3] Landis E. M., “O printsipe Fragmena–Lindelefa dlya reshenii ellipticheskikh uravnenii”, DAN SSSR, 107:4 (1956), 508–511 | MR | Zbl