In this note, by means of a kernel function induced by a continuous function f on the unit circle, we show that corresponding integral operator on Banach space A P is bounded or compact precisely when f belongs to the big Zygmund class Λ * or the little Zygmund class λ * , where A P consists of all holomorphic functions ϕ on C\S 1 with the finite corresponding norm. This generalizes the result in Hu, Song, Wei and Shen (2013) [5] and meanwhile may be considered as the infinitesimal version of main result obtained in Tang and Wu (2019) [8].