$$H^p$$Hp Boundedness of Multilinear Spectral Multipliers on Stratified Groups

Abstract

As far as we know, there is no study about $$H^p$$Hp boundedness of multilinear spectral multipliers on nilpotent Lie groups. In this paper, on stratified groups G, we prove a Hörmander type multiplier theorem for multilinear spectral multipliers on Hardy spaces, i.e., the boundedness from $$H^{p_1}\\times H^{p_2} \\times \\cdots \\times H^{p_N}$$Hp1×Hp2×⋯×HpN to $$L^p$$Lp with $$0<p_1,\\ldots ,p_N,p \\leqslant \\infty $$0<p1,…,pN,p⩽∞.