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Multilinear embedding - convolution estimates on smooth submanifolds


Author: William Beckner
Journal: Proc. Amer. Math. Soc. 142 (2014), 1217-1228
MSC (2010): Primary 35A15, 42B10, 58J70
DOI: https://doi.org/10.1090/S0002-9939-2013-11877-0
Published electronically: December 27, 2013
MathSciNet review: 3162244
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Abstract: Multilinear embedding estimates for the fractional Laplacian are obtained in terms of functionals defined over a hyperbolic surface. Convolution estimates used in the proof enlarge the classical framework of the convolution algebra for Riesz potentials to include the critical endpoint index and provide new realizations for fractional integral inequalities that incorporate restriction to smooth submanifolds. Results developed here are modeled on the space-time estimate used by Klainerman and Machedon in their proof of uniqueness for the Gross-Pitaevskii hierarchy.


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Additional Information

William Beckner
Affiliation: Department of Mathematics, The University of Texas at Austin, 1 University Station C1200, Austin, Texas 78712-0257
Email: beckner@math.utexas.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-11877-0
Received by editor(s): January 3, 2012
Received by editor(s) in revised form: April 27, 2012
Published electronically: December 27, 2013
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2013 American Mathematical Society

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