We consider the g-function related to a class of radial functions which gives a characterization of the L^p-norm of a function on the Heisenberg group.
The boundedness of maximal multilinear commutator on certain weighted spaces is obtained. The boundedness of mulitilinear commutators of singular integrals with Calderon-Zygmund kernel on Herz-type spaces is also considered.
Let b^→=(b1,…,bm),bi∈∧°βi(R^n),1≤i≤m,0〈βi〈β,0〈β〈1,[B^→,T]f(x)=∫R^n(b1(x)-b1(y))…(bm(x)-bm(y))K(x-y)f(y)dy,where K is a Calder6n-Zygmund kernel. In this paper, we show that [b^→,T] is bounded from L^p(R^n) to Fp^β,∞(R^n),as well as [b^→,1α]form L^p (R^n) to Fp^β,∞(R^n),where 1/q=1/p-α/n.