Multilinear embedding – convolution estimates on smooth submanifolds

Beckner, William

doi:10.1090/S0002-9939-2013-11877-0

Multilinear embedding – convolution estimates on smooth submanifolds
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by William Beckner PDF

Proc. Amer. Math. Soc. 142 (2014), 1217-1228 Request permission

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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