On multilinear determinant functionals

2009/11/06 by Philip T. Gressman, Gressman, Philip T.
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.0911.1283

openalex publication_date 2009/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper considers the problem of L^p-estimates for a certain multilinear functional involving integration against a kernel with the structure of a determinant. Examples of such objects are ubiquitous in the study of Fourier restriction and geometric averaging operators. It is shown that, under very general circumstances, the boundedness of such functionals is equivalent to a geometric inequality for measures which has recently appeared in work by D. Oberlin (Math Proc. Cambridge. Philos. Soc., 129, 2000) and Bak, Oberlin, and Seeger (J. Aust. Math. Soc., 85, 2008).

Citations

• Heat-flow monotonicity of Strichartz norms

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