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Bounds of Riesz Transforms on $L^p$ Spaces for Second Order Elliptic Operators

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Zhongwei Shen

Analysis of PDEs · Submitted 21 Oct 2004

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

The authors' main claim For any fixed $p>2$, a necessary and sufficient condition is obtained for the boundedness of the Riesz transforms associated with second order elliptic operators with real, symmetric, bounded measurable coefficients.

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arXiv IDmath/0410475 (version 1)
Pith IDG36P56EM, Pith's permanent record of this paper and its review
CitationZhongwei Shen. "Bounds of Riesz Transforms on $L^p$ Spaces for Second Order Elliptic Operators." arXiv:math/0410475 (2004). https://pith.science/paper/G36P56EM
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,647 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.29 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.05 · mentions code or data availability 0.01.

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

For any fixed $p>2$, a necessary and sufficient condition is obtained for the boundedness of the Riesz transforms associated with second order elliptic operators with real, symmetric, bounded measurable coefficients.

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 For any fixed $p>2$, a necessary and sufficient condition is obtained for the boundedness of the Riesz transforms associated with second order elliptic operators with real, symmetric, bounded measurable coefficients. result 0.87 0.91 0.89 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · 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

For any fixed $p>2$, a necessary and sufficient condition is obtained for the boundedness of the Riesz transforms associated with second order elliptic operators with real, symmetric, bounded measurable coefficients.

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