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Inequality for Burkholder's martingale transform

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Paata Ivanisvili

Analysis of PDEs · Submitted 19 Feb 2014

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

The authors' main claim We find the sharp constant $C=C(\tau,p, \mathbb{E}G, \mathbb{E}F)$ of the following inequality $\|(G^{2}+ \tau^{2} F^{2})^{1/2} \|_{p} \leq C \|F\|_{p},$ where $G$ is the transform of a martingale $F$ under a predictable sequence $\varepsilon$ with absolute value 1, $1<p< 2$, and $\tau$ is any real number.

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arXiv ID1402.4751 (version 2)
Pith IDVX6F2KLA, Pith's permanent record of this paper and its review
CitationPaata Ivanisvili. "Inequality for Burkholder's martingale transform." arXiv:1402.4751 (2014). https://pith.science/paper/VX6F2KLA
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,857 input tokens, $0.0001 reported.

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arXiv listing abstract v2. Results and the main claim are underlined; .

We find the sharp constant $C=C(\tau,p, \mathbb{E}G, \mathbb{E}F)$ of the following inequality $\|(G^{2}+ \tau^{2} F^{2})^{1/2} \|_{p} \leq C \|F\|_{p},$ where $G$ is the transform of a martingale $F$ under a predictable sequence $\varepsilon$ with absolute value 1, $1<p< 2$, and $\tau$ is any real number.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We find the sharp constant $C=C(\tau,p, \mathbb{E}G, \mathbb{E}F)$ of the following inequality $\|(G^{2}+ \tau^{2} F^{2})^{1/2} \|_{p} \leq C \|F\|_{p},$ where $G$ is the transform of a martingale $F$ under a predictable sequence $\varepsilon$ with absolute value 1, $1<p< 2$, and $\tau$ is any real number. result 0.62 0.95 0.91 asserted 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 find the sharp constant $C=C(\tau,p, \mathbb{E}G, \mathbb{E}F)$ of the following inequality $\|(G^{2}+ \tau^{2} F^{2})^{1/2} \|_{p} \leq C \|F\|_{p},$ where $G$ is the transform of a martingale $F$ under a predictable sequence $\varepsilon$ with absolute value 1, $1<p< 2$, and $\tau$ is any real number.

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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

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Cites it as background 1 paper
  • See also the works of Arnold [ref] for relations with contact geometry, the book of Ovsienko and Tabachnikov [ref] for projective geometric aspects, Angenent [ref] for connections with mean curvature flow, which are also discussed in [ref] , and Ivanisvili et al. [ref] for applications to the study of Bellman functions.

    Boundary torsion and convex caps of locally convex surfaces · Introduction · 1.00

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