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Discrete Hardy-type Inequalities

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Zhong-Wei Liao

Functional Analysis · Submitted 8 Jun 2014

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

The authors' main claim An improved factor is presented, which is smaller than the known one and is best possible.

how it is stated · asserted 1.00 read the record →

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arXiv ID1406.1984 (version 2)
Pith IDQPFVYXRO, Pith's permanent record of this paper and its review
CitationZhong-Wei Liao. "Discrete Hardy-type Inequalities." arXiv:1406.1984 (2014). https://pith.science/paper/QPFVYXRO
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,678 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.27 · compares with prior results 0.94 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

This paper studies the Hardy-type inequalities on the discrete intervals. The first result is the variational formulas of the optimal constants. Using these formulas, one may obtain an approximating procedure and the known basic estimates of the optimal constants. The second result, which is the main innovation of this paper, is about the factor of basic upper estimates. An improved factor is presented, which is smaller than the known one and is best possible. Some comparison results are included for comparing the optimal constants on different intervals.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 This paper studies the Hardy-type inequalities on the discrete intervals. background 0.67 0.79 0.03 asserted 0.98
s1 The first result is the variational formulas of the optimal constants. result 0.98 0.90 0.05 asserted 1.00
s2 Using these formulas, one may obtain an approximating procedure and the known basic estimates of the optimal constants. method 0.72 0.56 0.04 hedged possibility 1.00
s3 The second result, which is the main innovation of this paper, is about the factor of basic upper estimates. contribution 0.67 0.89 0.51 asserted 1.00
s4 An improved factor is presented, which is smaller than the known one and is best possible. result 0.92 0.93 0.52 asserted 1.00
s5 Some comparison results are included for comparing the optimal constants on different intervals. result 0.71 0.82 0.03 asserted 0.97

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

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

This paper studies the Hardy-type inequalities on the discrete intervals. The first result is the variational formulas of the optimal constants. Using these formulas, one may obtain an approximating procedure and the known basic estimates of the optimal constants. The second result, which is the main innovation of this paper, is about the factor of basic upper estimates. An improved factor is presented, which is smaller than the known one and is best possible. Some comparison results are included for comparing the optimal constants on different intervals.

Human review

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How the literature uses it

1 arXiv paper cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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