Multilinear and multiparameter spectral multipliers on stratified groups

Abstract

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 Hörmander‐type multiplier theorem for multilinear and multiparameter spectral multipliers on nilpotent Lie groups. In this paper, on product spaces of stratified groups G = G1 × ⋯ × GM, we prove Hörmander‐type multiplier theorems for multilinear and multiparameter spectral multipliers from to Lr(G) with , from to with , and from to Lr(·)(G) with or for all ℓ = 1,…,N.