A note on an integral operator induced by Zygmund function

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 AP is bounded or compact precisely when f belongs to the big Zygmund class ?* or the little Zygmund class lambda*, where AP consists of all holomorphic functions phi on C\S1 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].

Automated summary

In this note, the author demonstrates that the integral operator on Banach space AP is bounded or compact depending on whether the continuous function f belongs to the big Zygmund class ?* or the little Zygmund class lambda*. This finding generalizes previous research and serves as the infinitesimal version of another main result.