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arXiv · 2310.01059

Boundedness and compactness of Hausdorff operators on Fock spaces

Óscar Blasco·Antonio Galbis
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Abstract

We obtain a complete characterization of the bounded Hausdorff operators acting on a Fock space $F^p_\alpha$ and taking its values into a larger one $F^q_\alpha,\ 0 < p \leq q \leq \infty,$ as well as some necessary or sufficient conditions for a Hausdorff operator to transform a Fock space into a smaller one. Some results are written in the context of mixed norm Fock spaces. Also the compactness of Hausdorff operators on a Fock space is characterized. The compactness result for Hausdorff operators on the Fock space $F^\infty_\alpha$ is extended to more general Banach spaces of entire functions with weighted sup norms defined in terms of a radial weight and conditions for the Hausdorff operators to become $p$-summing are also included.

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Óscar Blasco, Antonio Galbis. 2023-10-02. Boundedness and compactness of Hausdorff operators on Fock spaces. https://arxiv.org/abs/2310.01059

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