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arXiv · 2505.04043

Hausdorff operators on weighted Bergman and Hardy spaces

Ha Duy Hung·Luong Dang Ky
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Abstract

Let $1\leq p<\infty$, $α>-1$, and let $φ$ be a measurable function on $(0,\infty)$. The main purpose of this paper is to study the Hausdorff operator \[ \mathscr H_φf(z)=\int_0^\infty f\left(\frac{z}{t}\right) \frac{φ(t)}{t} dt, \quad z\in \mathbb C^+, \] on the weighted Bergman space $\mathcal A^p_α(\mathbb C_+)$ and on the power weighted Hardy space $\mathcal H^p_{|\cdot|^α}(\mathbb{C_+})$ of the upper half-plane. Some applications to the real version of $\mathscr H_φ$ are also given.

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Ha Duy Hung, Luong Dang Ky. 2025-05-17. Hausdorff operators on weighted Bergman and Hardy spaces. https://arxiv.org/abs/2505.04043

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