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

In this paper, on Lie groups of polynomial growthG, we prove the boundedness ofmultilinear spectralmultipliers from the product of Besov spaces B-p1,q1(s1) (G) x B-p2,q2(s2) (G)x . . . x B-pN,qN(sN) (G) to Lebesgue spaces L-p(G) with p(1), . . . , p(N), q(1), . . . , q(N), p >= 1 and s(1), . . . , s(N) is an element of R. Then we prove the boundedness from the product of Triebel-Lizorkin spaces T-p1,q1(s1) (G) x T-p2,q2(s2) (G) x . . . x T-pN,qN(sN) (G) to Lebesgue spaces L-p(G) with p(1), . . . , p(N), q(1), . . . , q(N) > 1, p >= 1, s1, . . , s(N) is an element of R.