On multilinear determinant functionals
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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.References
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Additional Information
- Philip T. Gressman
- Affiliation: Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19103
- MR Author ID: 690453
- Email: gressman@math.upenn.edu
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2473-2484
- MSC (2010): Primary 28A75, 47G10; Secondary 42B10
- DOI: https://doi.org/10.1090/S0002-9939-2010-10656-1
- MathSciNet review: 2784813