Fractional Integrals Associated with Radon Transforms
Boris Rubin
TL;DR
This paper establishes precise bounds for fractional integrals linked to Radon transforms in multi-dimensional space, using advanced interpolation techniques for operator families.
Contribution
It provides the first sharp norm estimates for these fractional integrals associated with three types of Radon transforms.
Findings
Sharp norm estimates for fractional Radon integrals
Application of interpolation results to operator analysis
Extension to multiple types of Radon transforms
Abstract
We obtain sharp norm estimates for fractional integrals generated by Radon transforms of three types in the n-dimensional real Euclidean space. The method relies on recent interpolation results for analytic families of operators.
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Taxonomy
TopicsNumerical methods in inverse problems · Advanced Harmonic Analysis Research · Mathematical Analysis and Transform Methods