An extension theorem for $H^{p}$ functions

Abstract:

Let V be a pure $(n - 1)$-dimensional variety in the polydisc ${U^n}$ with the distance from V to the torus ${\text {II}^n}$ positive and assume f is analytic on $\Omega \equiv {U^n}\backslash V$ Further let $u(z)$ be the real part of a function g analytic on $\Omega$ and assume $|f(z){|^p} \leqq u(z)$ for $z \in \Omega$. Then f can be analytically extended to a function $\hat f$ in ${H^p}({U^n})$.