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

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Duong Quoc Huy, Luong Dang Ky

Classical Analysis and ODEs · Submitted 7 May 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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 $L^p(\mathbb R^n)$, $p\in [1,\infty]$.

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arXiv ID1705.02548 (version 2)
Pith IDH4LOY6P2, Pith's permanent record of this paper and its review
CitationDuong Quoc Huy, Luong Dang Ky. "The multi-parameter Hausdorff operators on $H^1$ and $L^p$." arXiv:1705.02548 (2017). https://pith.science/paper/H4LOY6P2
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,094 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.27 · compares with prior results 0.93 · mentions code or data availability 0.01.

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arXiv listing abstract v2. Results and the main claim are underlined; .

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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#sentencerolethe authors' own workstates the main conclusionstrength
s0 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 $L^p(\mathbb R^n)$, $p\in [1,\infty]$. contribution 0.95 0.91 0.76 asserted 0.99
s1 The corresponding operator norms are also obtained. result 0.96 0.94 0.09 asserted 1.00
s2 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}. contribution 0.73 0.89 0.19 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original 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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