Extremizers of a Radon Transform Inequality
Extremizers of a Radon Transform Inequality
This chapter discusses the extremizers of a Radon transform inequality. The model for this analysis is Lieb's characterization of extremizers for the Hardy–Littlewood–Sobolev inequality for certain pairs of exponents. The chapter first introduces the four main steps of this model and sets up an endpoint inequality, before developing the identities to be used for the analysis in the remainder of this chapter. It then discusses some preliminary facts concerning extremizers and brings up direct and inverse Steiner symmetrization. Finally, the chapter returns to the inequality described in the first part of the chapter and begins the process of identifying extremizers for it. It concludes with further discussion on compact subgroups of the affine group as well as critical points.
Keywords: extremizers, inequalities, Radon transform, Radon transform inequality, Steiner symmetrization, affine group, critical points
Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.
Please, subscribe or login to access full text content.
If you think you should have access to this title, please contact your librarian.
To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.
