Convolution estimates for singular measures and some global nonlinear Brascamp—Lieb inequalities

Convolution estimates for singular measures and some global nonlinear Brascamp—Lieb inequalities
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奇异测度和一些全局非线性 Brascamp-Lieb 不等式的卷积估计

DOI：
10.1017/s0308210515000323
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发表时间：
2014
期刊：
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
影响因子：
--
通讯作者：
S. Steinerberger
S. Steinerberger
中科院分区：
--
文献类型：
--
作者：
H. Koch;S. Steinerberger

文献摘要

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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.