Interpolation by holomorphic functions in the unit ball with polynomial growth (Q1383404)

Let \(H(\mathbb{B}^n)\) be the space of holomorphic functions in \(\mathbb{B}^n= \{z\in \mathbb{C}^n: | z|<1\}\). The author considers the two following problems. The first one is connected with the investigation of the interpolation of holomorphic functions in the space \(A^{-\infty}= \bigcup_{p>0} A^{-p}\) where \[ A^{-p}= \{f\in H(\mathbb{B}^n): \| f\|_{A^{-p}}=: \sup_{z\in\mathbb{B}^n} (1-| z|)^p| f(z)|<+\infty\}. \] The second one concerns the extension of a holomorphic function from an analytic variety of complex dimension \(n-1\) in \(\mathbb{B}^n\) to a function in the ball.