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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On multilinear determinant functionals


Author: Philip T. Gressman
Journal: Proc. Amer. Math. Soc. 139 (2011), 2473-2484
MSC (2010): Primary 28A75, 47G10; Secondary 42B10
Published electronically: December 6, 2010
MathSciNet review: 2784813
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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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Additional Information

Philip T. Gressman
Affiliation: Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19103
Email: gressman@math.upenn.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10656-1
PII: S 0002-9939(2010)10656-1
Received by editor(s): April 5, 2010
Received by editor(s) in revised form: June 20, 2010
Published electronically: December 6, 2010
Additional Notes: The author was supported in part by NSF Grant DMS-0850791.
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.