Sobolev improving for averages over curves in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:math>

Beltran, David; Guo, Shaoming; Hickman, Jonathan; Seeger, Andreas

doi:10.1016/j.aim.2021.108089

Cited by 10 publications

(20 citation statements)

References 14 publications

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“…respectively. This definition is motivated by our related work on L p Sobolev estimates for the moment curve in four dimensions [1]. Note that γ is a primitive for γ Ò in the sense that γ1 " γ Ò .…”

Section: `Aă0mentioning

confidence: 99%

“…If we take mpµq to be the integer which minimises |2 ´ℓm ´G2 ps µ q|, then we obtain (8.31). On the other hand, the Frenet equations ensure that G 2 psq " e 33 psq ´1e 32 psq satisfies |G 1 2 psq| " 1 for all s P I 0 . Consequently, the assignment µ Þ Ñ mpµq is Op1q-to-1, as claimed.…”

Section: `Aă0mentioning

confidence: 99%

“…Theorem 1.2. Suppose γ : I Ñ R 3 is a smooth, non-degenerate space curve and let 3 ď p ď 4 and σ ă σppq where σppq :" 1 5 `1 `2 p ˘. Then A γ maps L p pR 3 q boundedly into L p σ pR 4 q.…”

mentioning

confidence: 99%

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Sharp $L^p$ bounds for the helical maximal function

Beltrán¹,

Guo²,

Hickman³

et al. 2021

Preprint

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Section: `Aă0mentioning

confidence: 99%

Section: `Aă0mentioning

confidence: 99%

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Sharp $L^p$ bounds for the helical maximal function

Beltrán¹,

Guo²,

Hickman³

et al. 2021

Preprint

Self Cite

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“…By this observation, we are naturally led to regard the operators U θ ± , U 0 ± as variable coefficient generalizations of the associated conic surfaces. Meanwhile, the decoupling inequalities for the extension (adjoint restriction) operators given by these conic surfaces, which are constant coefficient counterparts of the abovementioned operators, are already known (see Theorem 3.1 below and [1]). Those inequalities were, in fact, deduced from the decoupling inequality for the nondegenerate curve due to Bourgain, Demeter, and Guth [6].…”

Section: Introductionmentioning

confidence: 99%

“…Let I = [1,2]. We consider the maximal operator Mf (x) = sup (θ,t,s)∈T×I 2 |f * σ θ t,s (x)|, which was called the elliptic maximal function in [8].…”

Section: Introductionmentioning

confidence: 99%

Routine colonoscopy may be needed for uncomplicated acute right colonic diverticulitis

Lee

Park

et al. 2020

Preprint

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BACKGROUND: Routine colonoscopy is recommended to determine the coexistence of colon cancer after medical treatment for colon diverticulitis. However, in the case of uncomplicated diverticulitis diagnosed by computed tomography imaging, the clinical relevance of routine follow-up colonoscopy has recently been debated. Yet, the role of follow-up colonoscopy for right colon diverticulitis, which tends to develop at a younger age than left colon diverticulitis, has not been specifically evaluated. Therefore, our aim in this study was to evaluate the incidence of right colon cancer or colonic adenomatous polyps, detected by routine colonoscopy, after conservative management of acute uncomplicated right colon diverticulitis. METHODS: Included were patients with uncomplicated right colon diverticulitis diagnosed by computed tomography imaging, between 2011 and 2017, and who underwent follow-up colonoscopy surveillance after treatment. The primary outcome was the incidence of colon cancer, with the detection rate of adenoma being the secondary outcome. Information for analysis was retrieved, retrospectively, from patients’ medical records. RESULTS: The study group included 330 consecutive patients, with a mean age of 41.9 years, and 51.9% being men. For the primary outcome, the rate of colon cancer on follow-up colonoscopy was 0.3% (1/330 cases). The rate of adenoma detection was 20.9% (69/330 cases), with advanced adenoma, including colon cancer, observed in 9 patients (2.7%). CONCLUSION: In patients with acute uncomplicated right colonic diverticulitis, routine colonoscopy after conservative treatment may be necessary because although the colon cancer detection rate is low, it is possible to detect advanced colon adenoma.

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Wave front sets of Riesz type on Minkowski space

Fan,

Dai,

2024

J. Pseudo-Differ. Oper. Appl.

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Sobolev improving for averages over curves in R4

Cited by 10 publications

References 14 publications

Sharp $L^p$ bounds for the helical maximal function

Sharp $L^p$ bounds for the helical maximal function

Routine colonoscopy may be needed for uncomplicated acute right colonic diverticulitis

Wave front sets of Riesz type on Minkowski space

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