On extremals for a Radon-like transform

2011/06/03 by Michael Christ, Christ, Michael · 2 citations
Mathematics · #Advanced Harmonic Analysis Research #Numerical methods in inverse problems #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1106.0728

Abstract

Convolution with an appropriate surface measure on a paraboloid in R^d defines a bounded operator T from L^p(R^d) to L^q(R^d) for certain exponents p,q. In this article it is proved that there exist functions which extremize the associated inequality.

Citations

• Existence of Extremals for a Fourier Restriction Inequality

Cited by

• A sharpened Hausdorff-Young inequality
• Extremizers for Fourier restriction inequalities: convex arcs

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• Quasiextremals for a Radon-like transform
• Extremizers of a Radon transform inequality
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• Convolution operators defined by singular measures on the motion group