Let V(z) be a complex-valued function on the complex plane ℂ satisfying the condition {pipe}V(z) - V(ζ){pipe} ≤ w{pipe}z - ζ{pipe}, z, ζ ε ℂ; ω ≥ 0 be a Muckenhoupt A _p weight on ℂ; i. e., the inequality, holds for any disk B, {pipe}B{pipe} = σ(B), and σ be the Lebesque measure on ℂ. We define the operator T* _n as follows: The main result of this work consists in deriving the estimate, where b(p, n) grows as a power of n.