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The optimal constants in Khintchine's inequality for the case 2<p<3

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Olaf Mordhorst

Functional Analysis · Submitted 28 Jan 2016

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

The authors' main claim In this article we want to treat the case 2<p<3 with their technique.

how it is stated · asserted 0.68 read the record →

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arXiv ID1601.07850 (version 1)
Pith IDETQVRHEN, Pith's permanent record of this paper and its review
CitationOlaf Mordhorst. "The optimal constants in Khintchine's inequality for the case 2<p<3." arXiv:1601.07850 (2016). https://pith.science/paper/ETQVRHEN
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,972 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.35 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.73 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

A mean step in Haagerup's proof for the optimal constants in Khintchine's inequality is to show integral inequalities of type $\int(g^s-f^s)\mathrm{d}\mu\geq 0$. F.L. Nazarov and A.N. Podkorytov made Haagerup's proof much more clearer for the case 0<p<2 by using a lemma on distribution functions. In this article we want to treat the case 2<p<3 with their technique.

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 A mean step in Haagerup's proof for the optimal constants in Khintchine's inequality is to show integral inequalities of type $\int(g^s-f^s)\mathrm{d}\mu\geq 0$. F.L. Nazarov and A.N. background 1.00 0.06 0.05 asserted 0.99
s1 Podkorytov made Haagerup's proof much more clearer for the case 0<p<2 by using a lemma on distribution functions. background 1.00 0.04 0.04 asserted 1.00
s2 In this article we want to treat the case 2<p<3 with their technique. contribution 0.98 0.45 0.14 asserted 0.68

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.98.

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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

A mean step in Haagerup's proof for the optimal constants in Khintchine's inequality is to show integral inequalities of type $\int(g^s-f^s)\mathrm{d}\mu\geq 0$. F.L. Nazarov and A.N. Podkorytov made Haagerup's proof much more clearer for the case 0<p<2 by using a lemma on distribution functions. In this article we want to treat the case 2<p<3 with their technique.

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