On conditions for the pluriharmonicity of the indicator of a holomorphic function of several variables

In this paper we consider holomorphic functions $f(z,w)$ defined in a domain $E_r\times T_\alpha$, where $E_r=\{z:|z|<r\}$ 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.
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