On multilinear determinant functionals - Mathematics > Classical Analysis and ODEsReport as inadecuate




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Abstract: This paper considers the problem of $L^p$-estimates for a certain multilinearfunctional involving integration against a kernel with the structure of adeterminant. Examples of such objects are ubiquitous in the study of Fourierrestriction and geometric averaging operators. It is shown that, under verygeneral circumstances, the boundedness of such functionals is equivalent to ageometric inequality for measures which has recently appeared in work by D.Oberlin Math Proc. Cambridge. Philos. Soc., 129, 2000 and Bak, Oberlin, andSeeger J. Aust. Math. Soc., 85, 2008.



Author: Philip T. Gressman

Source: https://arxiv.org/



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