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Some nonlinear Brascamp-Lieb inequalities and applications to harmonic analysis

Published 2009-06-11, updated 2010-09-09Version 3

We use the method of induction-on-scales to prove certain diffeomorphism invariant nonlinear Brascamp--Lieb inequalities. We provide applications to multilinear convolution inequalities and the restriction theory for the Fourier transform, extending to higher dimensions recent work of Bejenaru--Herr--Tataru and Bennett--Carbery--Wright.

Comments: 34 pages, exposition revised

Categories: math.CA

Subjects: 44A12, 42B10, 44A35

Keywords: harmonic analysis, diffeomorphism invariant nonlinear brascamp-lieb inequalities, applications, multilinear convolution inequalities, higher dimensions

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