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bilinear estimate

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Convolution estimates for singular measures and some global nonlinear Brascamp—Lieb inequalities
Part of
- Functions of several variables
- Manifolds
Herbert Koch, Stefan Steinerberger
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 145 / Issue 6 / December 2015

Published online by Cambridge University Press:

08 October 2015, pp. 1223-1237

Print publication:

December 2015
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We give an L2 x L2 → L2 convolution estimate for singular measures supported on transversal hypersurfaces in ℝn, which improves earlier results of Bejenaru et al. as well as Bejenaru and Herr. The quantities arising are relevant to the study of the validity of bilinear estimates for dispersive partial differential equations. We also prove a class of global, nonlinear Brascamp–Lieb inequalities with explicit constants in the same spirit.