Commutators of homogeneous fractional integrals on Herz-type Hardy spaces with variable exponent

Let Ω ∈ L ^s (S ^n?1), s ≥ 1, be a homogeneous function of degree zero, and let σ (0 < σ < n) and b be Lipschitz or BMO functions. In this paper, we establish the boundedness of the commutators b, T _Ω,σ ], generated by a homogeneous fractional integral operator T _Ω,σ and function b, on the Herz-type Hardy spaces with variable exponent.