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Dyadic-BMO functions, the dyadic Gurov-Reshetnyak conditions on $[0,1]^n$ and rearrangements of functions

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Eleftherios N. Nikolidakis

Classical Analysis and ODEs · Submitted 14 Oct 2014

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

The authors' main claim We introduce the space of dyadic bounded mean oscillation functions $f$ defined on $[0,1]^n$ and study the behavior of the nonincreasing rearrangement of $f$, as an element of the space $BMO((0,1])$.

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arXiv ID1410.4128 (version 1)
Pith ID4XWUQFMB, Pith's permanent record of this paper and its review
CitationEleftherios N. Nikolidakis. "Dyadic-BMO functions, the dyadic Gurov-Reshetnyak conditions on $[0,1]^n$ and rearrangements of functions." arXiv:1410.4128 (2014). https://pith.science/paper/4XWUQFMB
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,370 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We introduce the space of dyadic bounded mean oscillation functions $f$ defined on $[0,1]^n$ and study the behavior of the nonincreasing rearrangement of $f$, as an element of the space $BMO((0,1])$. We also study the analogous class of functions that satisfy the dyadic Gurov-Reshetnyak condition and look upon their integrability properties.

background contribution method result interpretation main claim

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We introduce the space of dyadic bounded mean oscillation functions $f$ defined on $[0,1]^n$ and study the behavior of the nonincreasing rearrangement of $f$, as an element of the space $BMO((0,1])$. contribution 1.00 0.91 0.16 asserted 0.98
s1 We also study the analogous class of functions that satisfy the dyadic Gurov-Reshetnyak condition and look upon their integrability properties. contribution 1.00 0.86 0.12 asserted 0.85

What kind of paper the classifier reports this is: theoretical result 0.96 · 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 introduce the space of dyadic bounded mean oscillation functions $f$ defined on $[0,1]^n$ and study the behavior of the nonincreasing rearrangement of $f$, as an element of the space $BMO((0,1])$. We also study the analogous class of functions that satisfy the dyadic Gurov-Reshetnyak condition and look upon their integrability properties.

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