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Functional Inequalities in Stratified Lie groups with Sobolev, Besov, Lorentz and Morrey spaces

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Diego Chamorro (LaMME), Anca-Nicoleta Marcoci, Liviu-Gabriel Marcoci

Functional Analysis · Submitted 22 May 2015

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

The authors' main claim These arguments can be generalized to many different frameworks, in particular the proofs are given in the setting of stratified Lie groups.

how it is stated · asserted 0.71 read the record →

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arXiv ID1505.05986 (version 3)
Pith IDNRJH4SCQ, Pith's permanent record of this paper and its review
CitationAnca-Nicoleta Marcoci, Diego Chamorro (LaMME), Liviu-Gabriel Marcoci. "Functional Inequalities in Stratified Lie groups with Sobolev, Besov, Lorentz and Morrey spaces." arXiv:1505.05986 (2015). https://pith.science/paper/NRJH4SCQ
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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, 4,208 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.15 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.09 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

The study of Sobolev inequalities can be divided in two cases: p = 1 and 1 < p < +$\infty$. In the case p = 1 we study here a relaxed version of refined Sobolev inequalities. When p > 1, using as base space classical Lorentz spaces associated to a weight from the Arino-Muckenhoupt class Bp, we will study Gagliardo-Nirenberg inequalities. As a by-product we will also consider Morrey-Sobolev inequalities. These arguments can be generalized to many different frameworks, in particular the proofs are given in the setting of stratified Lie groups.

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 The study of Sobolev inequalities can be divided in two cases: p = 1 and 1 < p < +$\infty$. background 1.00 0.08 0.03 asserted 1.00
s1 In the case p = 1 we study here a relaxed version of refined Sobolev inequalities. contribution 0.99 0.84 0.08 asserted 0.96
s2 When p > 1, using as base space classical Lorentz spaces associated to a weight from the Arino-Muckenhoupt class Bp, we will study Gagliardo-Nirenberg inequalities. contribution 0.88 0.79 0.15 asserted 0.94
s3 As a by-product we will also consider Morrey-Sobolev inequalities. contribution 0.85 0.80 0.08 asserted 0.88
s4 These arguments can be generalized to many different frameworks, in particular the proofs are given in the setting of stratified Lie groups. interpretation 0.49 0.81 0.16 asserted 0.71

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 v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • 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

The study of Sobolev inequalities can be divided in two cases: p = 1 and 1 < p < +$\infty$. In the case p = 1 we study here a relaxed version of refined Sobolev inequalities. When p > 1, using as base space classical Lorentz spaces associated to a weight from the Arino-Muckenhoupt class Bp, we will study Gagliardo-Nirenberg inequalities. As a by-product we will also consider Morrey-Sobolev inequalities. These arguments can be generalized to many different frameworks, in particular the proofs are given in the setting of stratified Lie groups.

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