Geodesic
On conditions for the pluriharmonicity of the indicator of a holomorphic function of several variables
Sbornik. Mathematics, Tome 27 (1975) no. 2, pp. 289-301 
P. Z. Agranovich; L. I. Ronkin. On conditions for the pluriharmonicity of the indicator of a holomorphic function of several variables. Sbornik. Mathematics, Tome 27 (1975) no. 2, pp. 289-301. http://geodesic.mathdoc.fr/item/SM_1975_27_2_a9/
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In this paper we consider holomorphic functions $f(z,w)$ defined in a domain $E_r\times T_\alpha$, where $E_r=\{z:|z| and $T_\alpha=\{w:|\arg w|<\alpha\}$; we obtain necessary and sufficient conditions for the pluriharmonicity of the indicator $$ h_f(z,w)=\varlimsup_{(z'w')\to(z,w)}\varlimsup_{t\to\infty}\frac{\ln|f(z',tw')|}{t^{\rho(t)}} $$ of $f(z,w)$ in $E_r\times T_\alpha$. We also obtain necessary and sufficient conditions for the pluriharmonicity of the indicator of a function $f(z)$ holomorphic in a cone. Bibliography: 6 titles.

[1] L. Gruman, “Entire functions of several variables and their asymptotic growth”, Arkiv för math., 9:1 (1971), 141–163 | DOI | MR | Zbl

[2] B. Ya. Levin, Raspredelenie kornei tselykh funktsii, Gostekhizdat, Moskva, 1956

[3] Brelo, Osnovy klassicheskoi teorii potentsiala, izd-vo «Mir», Moskva, 1964 | MR

[4] N. S. Landkof, Osnovy sovremennoi teorii potentsiala, izd-vo «Nauka», Moskva, 1966 | MR

[5] L. I. Ronkin, Vvedenie v teoriyu tselykh funktsii mnogikh peremennykh, izd-vo «Nauka», Moskva, 1971 | MR

[6] P. Lelong, “Fonctions plurisousharmoniques et fonctions analytiques de variables réeles”, Ann. Inst. Fourier, 11 (1961), 516–562 | MR