Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 35A15, 42B10, 58J70

Retrieve articles in all journals with MSC (2010): 35A15, 42B10, 58J70


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