Radial limits of $n$-subharmonic functions in the polydisc

Abstract:

We prove a relation between a certain weighted radial limit of an $n$-subharmonic function in the polydisc ${U^n}$ and the representing measure of its least $n$-harmonic majorant. We apply this result to functions in $N({U^n})$, the Nevalinna class of ${U^n}$. In particular, we obtain a necessary condition for a function to belong to the component of the origin in $N({U^n})$. These results are extensions of the work of J. H. Shapiro and A. L. Shields to $n > 1$.