Some weighted estimates for multilinear Fourier multiplier operators (Q2319346)

Summary: We first provide a weighted Fourier multiplier theorem for multilinear operators which extends Theorem 1.2 in [\textit{M. Fujita} and \textit{N. Tomita}, Trans. Am. Math. Soc. 364, No. 12, 6335--6353 (2012; Zbl 1275.42015)] by using \(L^r\)-based Sobolev spaces (\(1 < r \leq 2\)). Then, by using a different method, we obtain a result parallel to Theorem 6.2 which is an improvement of Theorem 1.2 under assumption (i) in [loc. cit.].