Multilinear Spectral Multipliers on Besov and Triebel–Lizorkin Spaces on Lie Groups of Polynomial Growth

In this paper, on Lie groups of polynomial growth G , we prove the boundedness of multilinear spectral multipliers from the product of Besov spaces B_p_1,q_1^s_1(G)× B_p_2,q_2^s_2(G) ×⋯× B_p_N,q_N^s_N(G) to Lebesgue spaces L^p(G) with p_1, … ,p_N,q_1, … ,q_N,p⩾ 1 and s_1, … ,s_N∈ℝ . Then we prove the boundedness from the product of Triebel–Lizorkin spaces T_p_1,q_1^s_1(G)× T_p_2,q_2^s_2(G) ×⋯× T_p_N,q_N^s_N(G) to Lebesgue spaces L^p(G) with p_1, … ,p_N,q_1, … ,q_N>1 , p⩾ 1 , s_1, … ,s_N∈ℝ .