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2-microlocal spaces associated with Besov type and Triebel-Lizorkin type spaces

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Koichi Saka

Functional Analysis · Submitted 8 Mar 2023

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

The authors' main claim We establish characterizations of these function spaces via the phi transform, the atom and molecular decomposition and wavelet decomposition.

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arXiv ID2303.04317 (version 1)
Pith IDP23YFQU3, Pith's permanent record of this paper and its review
CitationKoichi Saka. "2-microlocal spaces associated with Besov type and Triebel-Lizorkin type spaces." arXiv:2303.04317 (2023). https://pith.science/paper/P23YFQU3
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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.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,921 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.04 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · 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; .

In this papae we introduce and investigate new 2-microlocal spaces associated with Besov type and Triebel-LIzorkin type spaces. We establish characterizations of these function spaces via the phi transform, the atom and molecular decomposition and wavelet decomposition. As applications we consider the boundedness of the Calderon-Zygmund operator and the pseudo-differential operator on these function spaces

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 In this papae we introduce and investigate new 2-microlocal spaces associated with Besov type and Triebel-LIzorkin type spaces. contribution 1.00 0.92 0.12 asserted 0.98
s1 We establish characterizations of these function spaces via the phi transform, the atom and molecular decomposition and wavelet decomposition. result 0.51 0.94 0.38 asserted 1.00
s2 As applications we consider the boundedness of the Calderon-Zygmund operator and the pseudo-differential operator on these function spaces contribution 0.53 0.87 0.23 asserted 0.86

What kind of paper the classifier reports this is: theoretical result 0.90 · evidence from proof or derivation 1.00.

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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

In this papae we introduce and investigate new 2-microlocal spaces associated with Besov type and Triebel-LIzorkin type spaces. We establish characterizations of these function spaces via the phi transform, the atom and molecular decomposition and wavelet decomposition. As applications we consider the boundedness of the Calderon-Zygmund operator and the pseudo-differential operator on these function spaces

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