Analytic extension of a maximal surface in along its boundary.
Multilinear Fourier multipliers with minimal Sobolev regularity, I
We find optimal conditions on m-linear Fourier multipliers that give rise to bounded operators from products of Hardy spaces , , to Lebesgue spaces . These conditions are expressed in terms of L²-based Sobolev spaces with sharp indices within the classes of multipliers we consider. Our results extend those obtained in the linear case (m = 1) by Calderón and Torchinsky (1977) and in the bilinear case (m = 2) by Miyachi and Tomita (2013). We also prove a coordinate-type Hörmander integral condition...
Nonparametric estimation of the density of the alternative hypothesis in a multiple testing setup. Application to local false discovery rate estimation
In a multiple testing context, we consider a semiparametric mixture model with two components where one component is known and corresponds to the distribution of -values under the null hypothesis and the other component is nonparametric and stands for the distribution under the alternative hypothesis. Motivated by the issue of local false discovery rate estimation, we focus here on the estimation of the nonparametric unknown component in the mixture, relying on a preliminary estimator of the unknown...
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