Sur Les Suites D'Interpolation Pour Les Espaces De Bergman a Poids Dans la Boule De $\mathbb{C}^n$}

Abstract

Let $A$ be a sequence of points of $\mathbb{B}^n$ the unit ball in $\mathbb{C}^n.$ In terms of interpolating vectorial function (or Amar's function)[1], we give a necessary condition on $A$ to be interpolating for the weighted Bergman space $B^p_\alpha (\mathbb{B}^n). In the particular case of Hardy space $H^p (\mathbb{B}^2)$, this condition is sufficient no optimal. In the main theorem proof, we resolve Gleason's problem (vectorial form) in $B^p_\alpha (\mathbb{B}^n)$