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Convolution estimates for singular measures and some global nonlinear Brascamp-Lieb inequalities. (English) Zbl 1336.26014

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.

MSC:

26B15 Integration of real functions of several variables: length, area, volume
49Q15 Geometric measure and integration theory, integral and normal currents in optimization
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