On multilinear determinant functionals

Details On multilinear determinant functionals On multilinear determinant functionals

2009-11-06

arxiv.org/abs/0911.1283v1

Mathematics

Classical Analysis and ODEs

14 pages

Scientific paper

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).

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