On multilinear determinant functionals

Gressman, Philip

doi:10.1090/S0002-9939-2010-10656-1

On multilinear determinant functionals
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by Philip T. Gressman PDF

Proc. Amer. Math. Soc. 139 (2011), 2473-2484 Request permission

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 and by Bak, Oberlin, and Seeger.

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