Uniform estimates for the X-ray transform restricted to polynomial curves

Spyridon Dendrinos; Betsy Stovall

doi:10.1016/j.jfa.2012.03.020

Uniform estimates for the X-ray transform restricted to polynomial curves

Spyridon Dendrinos
, Betsy Stovall

Research output: Contribution to journal › Article › peer-review

Abstract

We establish near-optimal mixed norm estimates for the X-ray transform restricted to polynomial curves with a weight that is a power of the affine arclength. The bounds that we establish depend only on the spatial dimension and the degree of the polynomial. Some of our results are new even in the well-curved case.

Original language	English
Pages (from-to)	4986-5020
Number of pages	35
Journal	Journal of Functional Analysis
Volume	262
Issue number	12
DOIs	https://doi.org/10.1016/j.jfa.2012.03.020
Publication status	Published - 15 Jun 2012
Externally published	Yes

Keywords

Affine arclength
Generalized radon transform
Mixed norm
Restricted x-ray

Access to Document

10.1016/j.jfa.2012.03.020

Cite this

@article{a8abd907a43d4e90a53e95d9c8814421,

title = "Uniform estimates for the X-ray transform restricted to polynomial curves",

abstract = "We establish near-optimal mixed norm estimates for the X-ray transform restricted to polynomial curves with a weight that is a power of the affine arclength. The bounds that we establish depend only on the spatial dimension and the degree of the polynomial. Some of our results are new even in the well-curved case.",

keywords = "Affine arclength, Generalized radon transform, Mixed norm, Restricted x-ray",

author = "Spyridon Dendrinos and Betsy Stovall",

year = "2012",

month = jun,

day = "15",

doi = "10.1016/j.jfa.2012.03.020",

language = "English",

volume = "262",

pages = "4986--5020",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "12",

}

TY - JOUR

T1 - Uniform estimates for the X-ray transform restricted to polynomial curves

AU - Dendrinos, Spyridon

AU - Stovall, Betsy

PY - 2012/6/15

Y1 - 2012/6/15

N2 - We establish near-optimal mixed norm estimates for the X-ray transform restricted to polynomial curves with a weight that is a power of the affine arclength. The bounds that we establish depend only on the spatial dimension and the degree of the polynomial. Some of our results are new even in the well-curved case.

AB - We establish near-optimal mixed norm estimates for the X-ray transform restricted to polynomial curves with a weight that is a power of the affine arclength. The bounds that we establish depend only on the spatial dimension and the degree of the polynomial. Some of our results are new even in the well-curved case.

KW - Affine arclength

KW - Generalized radon transform

KW - Mixed norm

KW - Restricted x-ray

UR - https://www.scopus.com/pages/publications/84859817416

U2 - 10.1016/j.jfa.2012.03.020

DO - 10.1016/j.jfa.2012.03.020

M3 - Article

AN - SCOPUS:84859817416

SN - 0022-1236

VL - 262

SP - 4986

EP - 5020

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 12

ER -

Uniform estimates for the X-ray transform restricted to polynomial curves

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this