Cases of equality in certain multilinear inequalities of Hardy-Riesz-Brascamp-Lieb-Luttinger type
Michael Christ, Taryn C. Flock
TL;DR
This paper characterizes extremizing subsets for specific rearrangement inequalities related to Hardy, Riesz, and Brascamp-Lieb-Luttinger, extending previous work to special cases with minor corrections.
Contribution
It provides a new characterization of extremizers for certain multilinear inequalities, complementing earlier results by Burchard.
Findings
Identifies extremizing subsets for specific inequalities
Extends understanding of rearrangement inequalities in special cases
Includes minor corrections and clarifications to previous results
Abstract
Certain rearrangement inequalities of a type considered by Hardy, Riesz, and Brascamp-Lieb-Luttinger are studied. Subsets of the real line that extremize these inequalities are characterized. Our results apply only to special cases, and complement earlier results by Burchard treating other cases. This draft incorporates minor corrections and clarifications.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Mathematical Analysis and Transform Methods · Spectral Theory in Mathematical Physics