Uniform bounds for convolution and restricted X-ray transforms along degenerate curves

Spyridon Dendrinos; Betsy Stovall

doi:10.1016/j.jfa.2014.10.012

Uniform bounds for convolution and restricted X-ray transforms along degenerate curves

Spyridon Dendrinos
, Betsy Stovall

School of Mathematical Sciences

University of Wisconsin-Madison

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

Abstract

We establish endpoint Lebesgue space bounds for convolution and restricted X-ray transforms along curves satisfying fairly minimal differentiability hypotheses, with affine and Euclidean arclengths. We also explore the behavior of certain natural interpolants and extrapolants of the affine and Euclidean versions of these operators.

Original language	English
Pages (from-to)	585-633
Number of pages	49
Journal	Journal of Functional Analysis
Volume	268
Issue number	3
DOIs	https://doi.org/10.1016/j.jfa.2014.10.012
Publication status	Published - 1 Feb 2015

Keywords

Affine arclength
Generalized Radon transforms
Geometric inequalities

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10.1016/j.jfa.2014.10.012

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title = "Uniform bounds for convolution and restricted X-ray transforms along degenerate curves",

abstract = "We establish endpoint Lebesgue space bounds for convolution and restricted X-ray transforms along curves satisfying fairly minimal differentiability hypotheses, with affine and Euclidean arclengths. We also explore the behavior of certain natural interpolants and extrapolants of the affine and Euclidean versions of these operators.",

keywords = "Affine arclength, Generalized Radon transforms, Geometric inequalities",

author = "Spyridon Dendrinos and Betsy Stovall",

note = "Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

year = "2015",

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doi = "10.1016/j.jfa.2014.10.012",

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T1 - Uniform bounds for convolution and restricted X-ray transforms along degenerate curves

AU - Dendrinos, Spyridon

AU - Stovall, Betsy

PY - 2015/2/1

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N2 - We establish endpoint Lebesgue space bounds for convolution and restricted X-ray transforms along curves satisfying fairly minimal differentiability hypotheses, with affine and Euclidean arclengths. We also explore the behavior of certain natural interpolants and extrapolants of the affine and Euclidean versions of these operators.

AB - We establish endpoint Lebesgue space bounds for convolution and restricted X-ray transforms along curves satisfying fairly minimal differentiability hypotheses, with affine and Euclidean arclengths. We also explore the behavior of certain natural interpolants and extrapolants of the affine and Euclidean versions of these operators.

KW - Affine arclength

KW - Generalized Radon transforms

KW - Geometric inequalities

UR - https://www.scopus.com/pages/publications/84919487469

U2 - 10.1016/j.jfa.2014.10.012

DO - 10.1016/j.jfa.2014.10.012

M3 - Article

AN - SCOPUS:84919487469

SN - 0022-1236

VL - 268

SP - 585

EP - 633

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 3

ER -

Uniform bounds for convolution and restricted X-ray transforms along degenerate curves

Abstract

Keywords

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