Abstract
We study the Hausdorff operator
where \({\phi \in L_{\rm loc}^{1}((0,\infty ) \setminus \{1\})}\). We give a sufficient condition on \({\phi }\) such that \({H_{\phi }}\) is bounded on the Hardy space H 1. The result is an improvement of the main theorem in [10] and it negates that \({\int_{0}^{\infty }\frac{|\phi (u)|}{u} \,du < \infty}\) is a necessary and sufficient condition of boundedness of \({H_{\phi }}\) on H 1.
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Supported by NSFC(11471288,11371136) and NSFZJ (LY14A010015).
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Chen, J., Fan, D. & Zhu, X. The Hausdorff operator on the Hardy space \({H^{1}(\mathbb{R}^{1})}\) . Acta Math. Hungar. 150, 142–152 (2016). https://doi.org/10.1007/s10474-016-0622-1
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DOI: https://doi.org/10.1007/s10474-016-0622-1