English

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

Complex Variables 2008-07-02 v1

Abstract

Let AA be a sequence of points of Bn\mathbb{B}^n the unit ball in Cn.\mathbb{C}^n. In terms of interpolating vectorial function (or Amar's function)[1], we give a necessary condition on AA to be interpolating for the weighted Bergman space Bαp(Bn).IntheparticularcaseofHardyspaceB^p_\alpha (\mathbb{B}^n). In the particular case of Hardy space H^p (\mathbb{B}^2),thisconditionissufficientnooptimal.Inthemaintheoremproof,weresolveGleasonsproblem(vectorialform)in, 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)$

Keywords

Cite

@article{arxiv.0807.0154,
  title  = {Sur Les Suites D'Interpolation Pour Les Espaces De Bergman a Poids Dans la Boule De $\mathbb{C}^n$}},
  author = {Abdelkader El Hasnaoui},
  journal= {arXiv preprint arXiv:0807.0154},
  year   = {2008}
}

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22 pages