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arXiv · 1705.02548

The multi-parameter Hausdorff operators on $H^1$ and $L^p$

Duong Quoc Huy·Luong Dang Ky
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Abstract

In the present paper, we characterize the nonnegative functions $\varphi$ for which the multi-parameter Hausdorff operator $\mathcal H_\varphi$ generated by $\varphi$ is bounded on the multi-parameter Hardy space $H^1(\mathbb R\times\cdots\times\mathbb R)$ or $L^p(\mathbb R^n)$, $p\in [1,\infty]$. The corresponding operator norms are also obtained. Our results improve some recent results in \cite{FZ, LM2, LM3, We} and give an answer to an open question posted by Liflyand \cite{Li}.

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Duong Quoc Huy, Luong Dang Ky. 2017-05-07. The multi-parameter Hausdorff operators on $H^1$ and $L^p$. https://arxiv.org/abs/1705.02548

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