A NOTE ON AN INTEGRAL OPERATOR INDUCED BY ZYGMUND FUNCTION

Abstract

In this note, by means of a kernel function induced by a continuousfunction f on the unit circle, we show that corresponding integral operator onBanach space AP is bounded or compact precisely when fbelongs to the bigZygmund class Λ∗ or the little Zygmund class λ∗, whereAP consists of allholomorphic functions φ on C\S1 with the fifinite corresponding norm. Thisgeneralizes the result in Hu, Song, Wei and Shen (2013) [5] and meanwhilemay be considered as the infifinitesimal version of main result obtained in Tangand Wu (2019)