Convolution estimates for singular measures and some global nonlinear Brascamp—Lieb inequalities
Published online by Cambridge University Press: 08 October 2015
Abstract
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.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 6 , December 2015 , pp. 1223 - 1237
- Copyright
- Copyright © Royal Society of Edinburgh 2015
- 8
- Cited by