Pith. Sign in

RECORD

Hilbert transforms and maximal functions along flat curves on the Heisenberg group

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Lingxiao Zhang

Classical Analysis and ODEs · Submitted 16 Feb 2024

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

The authors' main claim We establish the $L^p$ boundedness of Hilbert transforms and maximal functions along flat curves in the Heisenberg group.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2402.10653 (version 1)
Pith IDEBS7SJJO, Pith's permanent record of this paper and its review
CitationLingxiao Zhang. "Hilbert transforms and maximal functions along flat curves on the Heisenberg group." arXiv:2402.10653 (2024). https://pith.science/paper/EBS7SJJO
Claim paper

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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,054 input tokens.

What the abstract itself states, as probabilities: claims first 0.10 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.32 · compares with prior results 0.98 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We establish the $L^p$ boundedness of Hilbert transforms and maximal functions along flat curves in the Heisenberg group. This generalizes the $\mathbb{R}^n$ result by Carbery, Christ, Vance, Wainger, and Watson. What is new about our result compared to the Heisenberg group generalization by Carbery, Wainger, and Wright is that we allow all three components of the curves to vary independently, we keep the original form of the conditions required in the $\mathbb{R}^n$ case, and our method is likely to be generalized to other stratified nilpotent 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 We establish the $L^p$ boundedness of Hilbert transforms and maximal functions along flat curves in the Heisenberg group. result 0.86 0.96 0.95 asserted 1.00
s1 This generalizes the $\mathbb{R}^n$ result by Carbery, Christ, Vance, Wainger, and Watson. interpretation 0.40 0.25 0.07 asserted 1.00
s2 What is new about our result compared to the Heisenberg group generalization by Carbery, Wainger, and Wright is that we allow all three components of the curves to vary independently, we keep the original form of the conditions required in the $\mathbb{R}^n$ case, and our method is likely to be generalized to other stratified nilpotent groups. contribution 0.99 0.88 0.10 hedged possibility 0.61

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 v1
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

We establish the $L^p$ boundedness of Hilbert transforms and maximal functions along flat curves in the Heisenberg group. This generalizes the $\mathbb{R}^n$ result by Carbery, Christ, Vance, Wainger, and Watson. What is new about our result compared to the Heisenberg group generalization by Carbery, Wainger, and Wright is that we allow all three components of the curves to vary independently, we keep the original form of the conditions required in the $\mathbb{R}^n$ case, and our method is likely to be generalized to other stratified nilpotent groups.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

1 arXiv paper cite this in 5 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

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.