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Dimension-free estimates on $l^2 (\mathbb{Z} ^d)$ for discrete dyadic maximal function over $l^1$ balls: small scales

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Jakub Niksiński

Classical Analysis and ODEs · Submitted 26 Nov 2023

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

The authors' main claim We give a dimension-free bound on $l^p(\mathbb{Z} ^d)$ for discrete Hardy-Littlewood operator over $l^1$ balls in $\mathbb{Z} ^d$ with small dyadic radii, where $p \in [2, \infty]$.

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arXiv ID2311.15442 (version 2)
Pith IDUORKKORA, Pith's permanent record of this paper and its review
CitationJakub Niksi\'nski. "Dimension-free estimates on $l^2 (\mathbb{Z} ^d)$ for discrete dyadic maximal function over $l^1$ balls: small scales." arXiv:2311.15442 (2023). https://pith.science/paper/UORKKORA
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,725 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.63 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.55 · compares with prior results 0.07 · mentions code or data availability 0.02.

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

We give a dimension-free bound on $l^p(\mathbb{Z} ^d)$ for discrete Hardy-Littlewood operator over $l^1$ balls in $\mathbb{Z} ^d$ with small dyadic radii, where $p \in [2, \infty]$.

background contribution method result interpretation main claim

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We give a dimension-free bound on $l^p(\mathbb{Z} ^d)$ for discrete Hardy-Littlewood operator over $l^1$ balls in $\mathbb{Z} ^d$ with small dyadic radii, where $p \in [2, \infty]$. result 0.70 0.94 0.87 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

The paper
Original abstract

We give a dimension-free bound on $l^p(\mathbb{Z} ^d)$ for discrete Hardy-Littlewood operator over $l^1$ balls in $\mathbb{Z} ^d$ with small dyadic radii, where $p \in [2, \infty]$.

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