Higher-order commutators of parametrized Littlewood–Paley operators on Herz spaces with variable exponent

Let $\Omega \in L^2\left(S^{n-1}\right)$ be a homogeneous function of degree zero and $b$ be a BMO or Lipschitz function. In this paper, we obtain some boundedness of the parametrized Littlewood–Paley operators and their high-order commutators on Herz spaces with variable exponent.