Abstract:

 We consider multilinear commutators of singular integrals defined by $T_{\vec{b}}f(x) =\int_{\mathbb{R}^n}\prod^m_{i=1}(b_i(x)-b_i(y))K(x, y)f(y)dy,$

where K is a standard Calder\'{o}n-Zygmund kernel, m is a positive integer and \vec{b} b =(b₁,b₂,...,b_m) is a family of m locally integrable functions. Based on the theory of
variable exponent and on generalization of the BMO norm, we prove the boundedness of
multilinear commutators T_{\vec{b}} on grand variable Herz spaces. The result is still new even in
the special case of m=1.

Key words: Grand Herz space, Variable exponent, Multilinear commutators