Multilinear and multiparameter spectral multipliers on stratified groups

作者：Fang, Jingxuan; Zhao, Jiman^*

来源：Mathematical Methods in the Applied Sciences, 2018, 41(13): 5327-5344.

DOI：10.1002/mma.5082

• Hormander-type condition
• multilinear and multiparameter spectral multipliers
• stratified groups
• variable Lebesgue spaces
• weighted Lebesgue spaces

As far as we know, the study of multilinear spectral multipliers on nilpotent Lie groups is a very new research work. There is even no study of Hormander-type multiplier theorem for multilinear and multiparameter spectral multipliers on nilpotent Lie groups. In this paper, on product spaces of stratified groups G=G(1)xxG(M), we prove Hormander-type multiplier theorems for multilinear and multiparameter spectral multipliers from Lp1(G)xxLpN(G) to L-r(G) with 1p1,,pN,r, from L1p1(G)xxLNpN(G) to Lr(G) with 1<p1,,pN,r, and from Lp1()(G)xxLpN()(G) to L-r()(G) with 1<p-p+ or 1p-p+< for all =1,...,N.

• 出版日期2018-9-15
• 单位北京师范大学