Boundedness of Singular Integral Operators on Herz-Morrey Spaces with Variable Exponent

Let $\Omega\in L^s(\mathrm{S}^{n-1}) \ (s>1)$ be a homogeneous function of degree zero and $b$ be a BMO function or Lipschitz function. In this paper, the authors obtain some boundedness of the Calder\''{o}n-Zygmund singular integral operator $T_\Omega$ and its commutator $b,T_\Omega]$ on Herz-Morrey spaces with variable exponent.