Geodesic
Boundedness conditions for entire functions of exponential type interior to the hyperoctant~$\mathbf R_+^n$
Izvestiya. Mathematics , Tome 34 (1990) no. 3, pp. 663-676

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Let $f(z)$ be an entire function on $\mathbf C^n$ of exponential type. This article contains an investigation of when the boundedness of $f$ on a subset dense in some sense in the positive hyperoctant $\mathbf R_+^n$ implies its boundedness on interior cones in $\mathbf R_+^n$. Bibliography: 13 titles. 
@article{IM2_1990_34_3_a6,
     author = {V. N. Logvinenko},
     title = {Boundedness conditions for entire functions of exponential type interior to the hyperoctant~$\mathbf R_+^n$},
     journal = {Izvestiya. Mathematics },
     pages = {663--676},
     publisher = {mathdoc},
     volume = {34},
     number = {3},
     year = {1990},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1990_34_3_a6/}
}
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V. N. Logvinenko. Boundedness conditions for entire functions of exponential type interior to the hyperoctant~$\mathbf R_+^n$. Izvestiya. Mathematics , Tome 34 (1990) no. 3, pp. 663-676. http://geodesic.mathdoc.fr/item/IM2_1990_34_3_a6/