On the linear extension property for interpolating sequences

2019/12/04 by Éric Amar, Amar, Eric
Mathematics · #32A35 #Algebraic and Geometric Analysis #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1912.01989

openalex publication_date 2019/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S be a sequence of points in Ω, where Ω is the unit ball or the unit polydisc in ℂⁿ. Denote H^p(Ω) the Hardy space of Ω. Suppose that S is H^p interpolating with p≥ 2. Then S has the bounded linear extension property. The same is true for the Bergman spaces of the ball by use of the "Subordination Lemma". The point of view used here is the vectorial one: Hilbertian and Besselian basis.

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