Holomorphic functions of several complex variables with nonnegative real part. Traces of holomorphic and pluriharmonic functions on the Shilov boundary

For a certain class of domains, conditions are given which a continuous function $\varphi$ on the Shilov boundary $S$ of a domain $D$ must satisfy in order that there exist a holomorphic (pluriharmonic) function $f$ in $D$, continuous on $\overline D$ and such that $f|_S=\varphi$.
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