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arXiv · 1702.03486

Norm of the Hausdorff operator on the real Hardy space $H^1(\mathbb R)$

Ha Duy Hung·Luong Dang Ky·Thai Thuan Quang
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Abstract

Let $φ$ be a nonnegative integrable function on $(0,\infty)$. It is well-known that the Hausdorff operator $\mathcal H_φ$ generated by $φ$ is bounded on the real Hardy space $H^1(\mathbb R)$. The aim of this paper is to give the exact norm of $\mathcal H_φ$. More precisely, we prove that $$\|\mathcal H_φ\|_{H^1(\mathbb R)\to H^1(\mathbb R)}= \int_0^\infty φ(t)dt.$$

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Ha Duy Hung, Luong Dang Ky, Thai Thuan Quang. 2017-02-12. Norm of the Hausdorff operator on the real Hardy space $H^1(\mathbb R)$. https://arxiv.org/abs/1702.03486

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