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Pré-Publication, Document De Travail Année : 2019

Random interpolating sequences in Dirichlet spaces

Nikolaos Chalmoukis
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Andreas Hartmann
Karim Kellay

Résumé

We discuss random interpolating sequences in weighted Dirichlet spaces $\mathcal{D}_\alpha$, $0\leq \alpha\leq 1$. Our results in particular imply that almost sure interpolating sequences for $\mathcal{D}_\alpha$ are exactly the almost sure separated sequences when $0\le \alpha<1/2$ (which covers the Hardy space $H^2=\mathcal{D}_0$), and they are exactly the almost sure zero sequences for $\mathcal{D}_\alpha$ when $1/2<\alpha<1$. We show that this last result remains valid in the classical Dirichlet space $\mathcal{D}=\mathcal{D}_1$ when one considers a weaker notion of interpolation, so-called simple interpolation. As a by-product we improve a sufficient condition by Rudowicz for random Carleson measures in Hardy spaces.
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Dates et versions

hal-02113238 , version 1 (28-04-2019)
hal-02113238 , version 2 (06-07-2019)
hal-02113238 , version 3 (23-09-2020)

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Nikolaos Chalmoukis, Andreas Hartmann, Karim Kellay, Brett D Wick. Random interpolating sequences in Dirichlet spaces. 2019. ⟨hal-02113238v1⟩
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