Extremizers of a Radon transform inequality
Michael Christ
TL;DR
This paper characterizes all extremizers of a specific Radon transform inequality at a critical endpoint, advancing understanding of the inequality's equality cases in harmonic analysis.
Contribution
It precisely identifies all extremizers for the Radon transform inequality at the endpoint case, a significant step in harmonic analysis.
Findings
All extremizers are explicitly characterized.
The extremizers are shown to be specific functions related to the geometry of the problem.
The result completes the understanding of equality cases for this Radon transform inequality.
Abstract
The Radon transform is a bounded operator from L^p of Euclidean space R^d to L^q of the Grassmann manifold of all affine hyperplanes in R^d, for certain exponents. We identify all extremizers of the associated inequality for the endpoint case p=(d+1)/d and q=d+1.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Numerical methods in inverse problems · Fatigue and fracture mechanics