Multilinear transference on product spaces and applications

Abstract

We establish transference results for multilinear Fourier multiplier operators from Euclidean spaces to product spaces of the form ${\mathbb{R}}^{d_1}\times {\mathbb{T}}^{d_2}$. We prove strong and weak-type transference principles that preserve the corresponding Euclidean operator bounds. As applications, we obtain bounds for certain multilinear operators, as well as for some multiplier operators arising naturally in PDEs.

arXiv comment16 pages