6533b86ffe1ef96bd12cdfcb

RESEARCH PRODUCT

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

Betsy StovallSpyridon Dendrinos

subject

Polynomial curvesPolynomialX-ray transformMixed normDegree (graph theory)Mathematical analysisMixed normPower (physics)Affine arclengthDimension (vector space)Mathematics - Classical Analysis and ODEsClassical Analysis and ODEs (math.CA)FOS: MathematicsRestricted X-rayAffine transformation42B25Generalized Radon transformAnalysisMathematics

description

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.

yearjournalcountryeditionlanguage
2012-06-01Journal of Functional Analysis
10.1016/j.jfa.2012.03.020http://dx.doi.org/10.1016/j.jfa.2012.03.020