Koch, Herbert; Steinerberger, Stefan Convolution estimates for singular measures and some global nonlinear Brascamp-Lieb inequalities. (English) Zbl 1336.26014 Proc. R. Soc. Edinb., Sect. A, Math. 145, No. 6, 1223-1237 (2015). Motivated by the study of the validity of bilinear estimates for dispersive partial differential equations, an \(L^2 \times L^2 \rightarrow L^2\) convolution estimate for singular measures supported on transversal hypersurfaces in \(\mathbb{R}^n\) is provided, improving some earlier results from the literature. Afterwards, the proposed method is employed for proving a new class of global nonlinear Brascamp-Lieb type inequalities with explicit constants. Reviewer: Sorin-Mihai Grad (Chemnitz) Cited in 6 Documents MSC: 26B15 Integration of real functions of several variables: length, area, volume 49Q15 Geometric measure and integration theory, integral and normal currents in optimization Keywords:convolution; Brascamp-Lieb inequality; Loomis-Whitney inequality; bilinear estimate; singular measure PDFBibTeX XMLCite \textit{H. Koch} and \textit{S. Steinerberger}, Proc. R. Soc. Edinb., Sect. A, Math. 145, No. 6, 1223--1237 (2015; Zbl 1336.26014) Full Text: DOI arXiv