Journal of the
Korean Mathematical Society JKMS

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

Keywords: Herz-type Hardy space, variable exponent, Calder\'{o}n-Zygmund singular integral, commutator

MSC numbers: Primary 46E30; Secondary 42B35, 42B20